# Solving models with rational and floating point.

Using [cobrapy](http://opencobra.github.io/cobrapy/) (version 0.4.0b1 or later), we have interfaces to serveral floating point solvers ([gurobi](http://www.gurobi.com), [MOSEK](http://www.mosek.com/), [CPLEX](http://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/), [Clp](https://projects.coin-or.org/Clp), and two different versions of [GLPK](https://www.gnu.org/software/glpk/)). Additionally, we can use the rational solving capabilities of GLPK and esolver (also known as [QSopt_ex](http://www.dii.uchile.cl/~daespino/ESolver_doc/main.html)). We will use all of these solvers on all the models in the collection.


```python
import os

from numpy import array
import pandas
import sympy

import cobra

pandas.set_option("display.max_rows", 100)
```

We will verify all of our solutions by writing out the Stoichiometrix matrix $\mathbf S$ using the [sympy](http://sympy.org/) symbolic math library. The total error will be equivalent to 
$$ \sum \left|\mathbf S \cdot v \right| $$


```python
def convert_to_rational(value):
    return sympy.Rational("%.15g" % value)

def construct_exact_S(model):
    # intialize to 0
    S = sympy.SparseMatrix(len(model.metabolites), len(model.reactions), 0)
    # populate with stoichiometry
    for i, r in enumerate(model.reactions):
        for met, value in r._metabolites.iteritems():
            S[model.metabolites.index(met), i] = convert_to_rational(value)
    return S

def total_error(S, v):
    return sum(abs(i) for i in S * v)
```

Some of these models were exported from [BiGG](http://bigg.ucsd.edu/bigg/export.pl) as SBML, and others were downloaded from their respective publications. All of the models are available in a [git repository](https://github.com/opencobra/m_model_collection). They were parsed into a single mat file by an [included script](load_models.ipynb).


```python
models = []
for filename in sorted(os.listdir("sbml3")):
    if not filename.endswith(".xml"):
        continue
    models.append(cobra.io.read_sbml_model(os.path.join("sbml3", filename)))
```

These models all compute rationally with esolver and also with the other floating point solvers, as shown below. They also compute with floating point solvers in the [COBRA toolbox](http://dx.doi.org/doi:10.1038/nprot.2011.308), as shown [here](http://nbviewer.ipython.org/github/opencobra/m_model_collection/blob/master/MATLAB.ipynb).


```python
results = {}
exact_results = {}
errors = {}
for m in models:
    S = construct_exact_S(m)
    S_float = m.to_array_based_model().S
    rational_solution = m.optimize(solver="esolver", rational_solution=True)
    rational_v = sympy.Matrix(rational_solution.x)
    exact_results[m.id] = {"Rational": rational_solution.f,
                           "Decimal": float(rational_solution.f),
                           "Error": total_error(S, rational_v),
                           # Ensure the upper and lwoer bounds are satisfied.
                           "Bounds": all([r.upper_bound >= value >= r.lower_bound
                                              for r, value in zip(m.reactions, rational_v)])}
    # solve this model with all the solvers
    solutions = {solver: m.optimize(solver=solver)
                 for solver in cobra.solvers.solver_dict}
    solutions["cglpk_exact"] = m.optimize(solver="cglpk", exact=True)
    # store the objective value and errors
    results[m.id] = {k: v.f for k, v in solutions.iteritems()}
    errors[m.id] = {k: sum(abs(S_float * array(v.x))) for k, v in solutions.iteritems()}
# format the results as pandas dataframes
exact_results = pandas.DataFrame.from_dict(exact_results).T
results = pandas.DataFrame.from_dict(results)
errors = pandas.DataFrame.from_dict(errors)
```

For all of these models, we can demonstrate they satisfy the model constraints using exact operations.

$$\sum\left|\mathbf S \cdot v\right| = 0$$


```python
abs(exact_results.Error).max()
```




    0



$$ub \ge v \ge lb$$


```python
exact_results.Bounds.all()
```




    True



Here are objective values of the rational results provided by esolver:


```python
exact_results[["Decimal", "Rational"]]
```




<div>
<table border="1" class="dataframe">
  <thead>
    <tr style="text-align: right;">
      <th></th>
      <th>Decimal</th>
      <th>Rational</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <th>AbyMBEL891</th>
      <td>119.233</td>
      <td>386664062500000/3242927908653</td>
    </tr>
    <tr>
      <th>AraGEM</th>
      <td>10</td>
      <td>10</td>
    </tr>
    <tr>
      <th>GSMN_TB</th>
      <td>0.1312623</td>
      <td>576559343750000/4392422515431629</td>
    </tr>
    <tr>
      <th>PpaMBEL1254</th>
      <td>78.70059</td>
      <td>4725000000000/60037666259</td>
    </tr>
    <tr>
      <th>PpuMBEL1071</th>
      <td>132.3654</td>
      <td>644062500000/4865793703</td>
    </tr>
    <tr>
      <th>STM_v1_0</th>
      <td>0.4778337</td>
      <td>178576000/373720009</td>
    </tr>
    <tr>
      <th>S_coilicolor_fixed</th>
      <td>860.0888</td>
      <td>408741530000000000/475231759036371</td>
    </tr>
    <tr>
      <th>SpoMBEL1693</th>
      <td>63.78566</td>
      <td>1237500000000/19400913101</td>
    </tr>
    <tr>
      <th>T_Maritima</th>
      <td>0.359469</td>
      <td>180000000/500738623</td>
    </tr>
    <tr>
      <th>VvuMBEL943</th>
      <td>96.40232</td>
      <td>14000000000/145224717</td>
    </tr>
    <tr>
      <th>iAC560</th>
      <td>4.042612</td>
      <td>35000000/8657769</td>
    </tr>
    <tr>
      <th>iAF1260</th>
      <td>0.7367009</td>
      <td>146888000/199386199</td>
    </tr>
    <tr>
      <th>iAF692</th>
      <td>0.02725005</td>
      <td>107424000/3942157643</td>
    </tr>
    <tr>
      <th>iAI549</th>
      <td>84.17419</td>
      <td>114000000000/1354334333</td>
    </tr>
    <tr>
      <th>iAN840m</th>
      <td>0.3401361</td>
      <td>50/147</td>
    </tr>
    <tr>
      <th>iAO358</th>
      <td>255.1805</td>
      <td>586000000000/2296413281</td>
    </tr>
    <tr>
      <th>iAbaylyiV4</th>
      <td>12.30655</td>
      <td>34263125839313509122373268880000000/2784138406...</td>
    </tr>
    <tr>
      <th>iBT721_fixed</th>
      <td>0.5</td>
      <td>1/2</td>
    </tr>
    <tr>
      <th>iBsu1103</th>
      <td>1229.657</td>
      <td>1687500000000000/1372333638281</td>
    </tr>
    <tr>
      <th>iCA1273</th>
      <td>0.7402418</td>
      <td>293776000/396864911</td>
    </tr>
    <tr>
      <th>iCB925</th>
      <td>0.1194276</td>
      <td>1614000000/13514458561</td>
    </tr>
    <tr>
      <th>iCR744</th>
      <td>41.47674</td>
      <td>179687500000/4332247261</td>
    </tr>
    <tr>
      <th>iCS291</th>
      <td>0.1405489</td>
      <td>38125/271258</td>
    </tr>
    <tr>
      <th>iCS400</th>
      <td>0.215639</td>
      <td>63750/295633</td>
    </tr>
    <tr>
      <th>iCac802</th>
      <td>0.209597</td>
      <td>99830000000/476294907501</td>
    </tr>
    <tr>
      <th>iFF708</th>
      <td>14.91711</td>
      <td>113942000000/7638344959</td>
    </tr>
    <tr>
      <th>iGB555_fixed</th>
      <td>127.7891</td>
      <td>142500000000000/1115118722693</td>
    </tr>
    <tr>
      <th>iHD666_fixed</th>
      <td>0.2556721</td>
      <td>163316006250/638771297231</td>
    </tr>
    <tr>
      <th>iIB711</th>
      <td>84.68841</td>
      <td>100000000000/1180799053</td>
    </tr>
    <tr>
      <th>iIT341</th>
      <td>0.6928127</td>
      <td>814668000000/1175884921963</td>
    </tr>
    <tr>
      <th>iJL432</th>
      <td>0.3287407</td>
      <td>3750000000/11407166737</td>
    </tr>
    <tr>
      <th>iJN678</th>
      <td>0.06314984</td>
      <td>869550000000/13769631712373</td>
    </tr>
    <tr>
      <th>iJN746</th>
      <td>3.679412</td>
      <td>40000000/10871301</td>
    </tr>
    <tr>
      <th>iJO1366</th>
      <td>0.9823718</td>
      <td>189480000/192880127</td>
    </tr>
    <tr>
      <th>iJP815</th>
      <td>0.861512</td>
      <td>179500000/208354621</td>
    </tr>
    <tr>
      <th>iJR904</th>
      <td>0.9219481</td>
      <td>6380800/6920997</td>
    </tr>
    <tr>
      <th>iJS747</th>
      <td>34.17266</td>
      <td>15000000000000/438947370703</td>
    </tr>
    <tr>
      <th>iKF1028</th>
      <td>0.517807</td>
      <td>1900000/3669321</td>
    </tr>
    <tr>
      <th>iLC915</th>
      <td>79.02123</td>
      <td>786562500000000/9953812160053</td>
    </tr>
    <tr>
      <th>iLL672</th>
      <td>3.475283</td>
      <td>62750000000/18056084533</td>
    </tr>
    <tr>
      <th>iMA871</th>
      <td>27.79298</td>
      <td>100000000000/3598031369</td>
    </tr>
    <tr>
      <th>iMA945</th>
      <td>79.58958</td>
      <td>5000000000/62822291</td>
    </tr>
    <tr>
      <th>iMB745</th>
      <td>0.03094245</td>
      <td>161000000/5203208413</td>
    </tr>
    <tr>
      <th>iMH551</th>
      <td>0.7750811</td>
      <td>27300000000/35222122883</td>
    </tr>
    <tr>
      <th>iMM1415</th>
      <td>1.363428</td>
      <td>110000/80679</td>
    </tr>
    <tr>
      <th>iMM904</th>
      <td>0.2878657</td>
      <td>145400000/505096641</td>
    </tr>
    <tr>
      <th>iMO1056</th>
      <td>1.047929</td>
      <td>100000000/95426353</td>
    </tr>
    <tr>
      <th>iMP429_fixed</th>
      <td>0.8044324</td>
      <td>7063000000/8780103713</td>
    </tr>
    <tr>
      <th>iND750</th>
      <td>0.09732338</td>
      <td>21000000/215775499</td>
    </tr>
    <tr>
      <th>iNJ661</th>
      <td>0.05219947</td>
      <td>894000/17126611</td>
    </tr>
    <tr>
      <th>iNJ661m</th>
      <td>0.0521992</td>
      <td>107280000/2055203801</td>
    </tr>
    <tr>
      <th>iNV213</th>
      <td>11.53886</td>
      <td>12500000000000000/1083295987243349</td>
    </tr>
    <tr>
      <th>iOG654</th>
      <td>0.3554469</td>
      <td>12500/35167</td>
    </tr>
    <tr>
      <th>iOR363</th>
      <td>250</td>
      <td>250</td>
    </tr>
    <tr>
      <th>iPP668</th>
      <td>3.891474</td>
      <td>95000000/24412341</td>
    </tr>
    <tr>
      <th>iPS189_fixed</th>
      <td>2.238961</td>
      <td>90000000/40197209</td>
    </tr>
    <tr>
      <th>iRC1080</th>
      <td>6.156851</td>
      <td>1000000000000000000000/162420679450988000257</td>
    </tr>
    <tr>
      <th>iRM588</th>
      <td>1000</td>
      <td>1000</td>
    </tr>
    <tr>
      <th>iRR1083</th>
      <td>77.94736</td>
      <td>1250000000/16036463</td>
    </tr>
    <tr>
      <th>iRS1563</th>
      <td>0.07996249</td>
      <td>16170000000000000000/202219826710707573821</td>
    </tr>
    <tr>
      <th>iRS1597</th>
      <td>8.969346</td>
      <td>37500000/4180907</td>
    </tr>
    <tr>
      <th>iRS605_fixed</th>
      <td>2.11678</td>
      <td>2051250000/969042437</td>
    </tr>
    <tr>
      <th>iRsp1095</th>
      <td>9.686899</td>
      <td>1514600000000000000000000/15635550882015213602...</td>
    </tr>
    <tr>
      <th>iSB619</th>
      <td>0.1580503</td>
      <td>10000/63271</td>
    </tr>
    <tr>
      <th>iSH335</th>
      <td>1.159211</td>
      <td>87700000000/75654904569</td>
    </tr>
    <tr>
      <th>iSO783</th>
      <td>17.92031</td>
      <td>100000000000/5580261343</td>
    </tr>
    <tr>
      <th>iSR432</th>
      <td>11.48257</td>
      <td>72500000000000000/6313917669853967</td>
    </tr>
    <tr>
      <th>iSS724</th>
      <td>22.42152</td>
      <td>5000/223</td>
    </tr>
    <tr>
      <th>iSS884</th>
      <td>70.35929</td>
      <td>7513000000000/106780503717</td>
    </tr>
    <tr>
      <th>iSyn669</th>
      <td>0.1790899</td>
      <td>6802000000/37980929237</td>
    </tr>
    <tr>
      <th>iTH366</th>
      <td>27890.89</td>
      <td>10741489258500000/385125386207</td>
    </tr>
    <tr>
      <th>iTL885</th>
      <td>7.098836</td>
      <td>697400000000/98241455449</td>
    </tr>
    <tr>
      <th>iTY425_fixed</th>
      <td>0.8868335</td>
      <td>5000000/5638037</td>
    </tr>
    <tr>
      <th>iVM679</th>
      <td>2.82657</td>
      <td>26520000000/9382396471</td>
    </tr>
    <tr>
      <th>iVS941_fixed</th>
      <td>0.5233846</td>
      <td>10000000/19106407</td>
    </tr>
    <tr>
      <th>iWV1314</th>
      <td>25.6824</td>
      <td>10504392200845731410/409011287584573141</td>
    </tr>
    <tr>
      <th>iWZ663</th>
      <td>34.07588</td>
      <td>350000000000/10271194511</td>
    </tr>
    <tr>
      <th>iYL1228</th>
      <td>1.042637</td>
      <td>1590492000/1525450603</td>
    </tr>
    <tr>
      <th>iYO844</th>
      <td>1.582798</td>
      <td>256250000000/161896806353</td>
    </tr>
    <tr>
      <th>iZM363</th>
      <td>2.532606</td>
      <td>181250000/71566597</td>
    </tr>
    <tr>
      <th>iZmobMBEL601</th>
      <td>0.3500804</td>
      <td>61718750/176298791</td>
    </tr>
    <tr>
      <th>mus_musculus</th>
      <td>129.1006</td>
      <td>10000000/77459</td>
    </tr>
    <tr>
      <th>textbook</th>
      <td>0.8739215</td>
      <td>686440/785471</td>
    </tr>
  </tbody>
</table>
</div>



Here is the $\sum\left|\mathbf S \cdot v\right|$ error computed using floating point operations for every solver. When computed rationally with esolver above, this value was exactly 0. Howver, when rounding the fractional values to floating point, there is a very small amount of resulting error, so even esolver does not give 0 error for this computation.


```python
errors.T
```




<div>
<table border="1" class="dataframe">
  <thead>
    <tr style="text-align: right;">
      <th></th>
      <th>cglpk</th>
      <th>cglpk_exact</th>
      <th>coin</th>
      <th>cplex</th>
      <th>esolver</th>
      <th>glpk</th>
      <th>gurobi</th>
      <th>mosek</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <th>AbyMBEL891</th>
      <td>1.030879e-11</td>
      <td>6.538390e-12</td>
      <td>3.057219e-11</td>
      <td>1.652062e-11</td>
      <td>6.093565e-12</td>
      <td>1.168024e-11</td>
      <td>2.098006e-11</td>
      <td>1.866628e-11</td>
    </tr>
    <tr>
      <th>AraGEM</th>
      <td>4.518242e-12</td>
      <td>3.761263e-12</td>
      <td>4.350840e-11</td>
      <td>1.031621e-11</td>
      <td>3.953687e-12</td>
      <td>5.721206e-12</td>
      <td>1.492412e-11</td>
      <td>1.607253e-11</td>
    </tr>
    <tr>
      <th>GSMN_TB</th>
      <td>3.265029e-10</td>
      <td>1.438631e-10</td>
      <td>4.422610e-10</td>
      <td>1.794655e-09</td>
      <td>1.318417e-10</td>
      <td>1.580843e-07</td>
      <td>2.451718e-09</td>
      <td>1.055735e-09</td>
    </tr>
    <tr>
      <th>PpaMBEL1254</th>
      <td>5.524246e-12</td>
      <td>5.503863e-12</td>
      <td>1.686022e-11</td>
      <td>1.653475e-11</td>
      <td>1.599098e-12</td>
      <td>5.808043e-12</td>
      <td>6.458234e-12</td>
      <td>1.327733e-11</td>
    </tr>
    <tr>
      <th>PpuMBEL1071</th>
      <td>9.213515e-12</td>
      <td>1.006636e-07</td>
      <td>2.682011e-11</td>
      <td>6.212253e-12</td>
      <td>5.611067e-12</td>
      <td>6.928756e-12</td>
      <td>1.996325e-11</td>
      <td>1.154134e-11</td>
    </tr>
    <tr>
      <th>STM_v1_0</th>
      <td>2.442772e-12</td>
      <td>7.615986e-09</td>
      <td>1.558550e-09</td>
      <td>6.747805e-13</td>
      <td>4.133462e-13</td>
      <td>4.027310e-12</td>
      <td>2.884140e-11</td>
      <td>1.424397e-11</td>
    </tr>
    <tr>
      <th>S_coilicolor_fixed</th>
      <td>6.094508e-11</td>
      <td>3.403941e-11</td>
      <td>1.417303e-10</td>
      <td>5.070666e-11</td>
      <td>3.497688e-11</td>
      <td>4.686266e-11</td>
      <td>5.399156e-11</td>
      <td>2.215057e-10</td>
    </tr>
    <tr>
      <th>SpoMBEL1693</th>
      <td>9.424184e-12</td>
      <td>6.328653e-12</td>
      <td>2.409888e-11</td>
      <td>7.634511e-12</td>
      <td>5.512237e-12</td>
      <td>8.155074e-12</td>
      <td>9.632115e-12</td>
      <td>2.056227e-11</td>
    </tr>
    <tr>
      <th>T_Maritima</th>
      <td>1.149696e-12</td>
      <td>1.017970e-09</td>
      <td>2.680799e-12</td>
      <td>1.312999e-12</td>
      <td>1.125577e-12</td>
      <td>1.578348e-12</td>
      <td>4.792797e-12</td>
      <td>1.448889e-11</td>
    </tr>
    <tr>
      <th>VvuMBEL943</th>
      <td>1.291556e-11</td>
      <td>1.200139e-11</td>
      <td>1.619902e-11</td>
      <td>5.522043e-12</td>
      <td>1.396693e-11</td>
      <td>8.099037e-12</td>
      <td>7.938761e-12</td>
      <td>2.371747e-11</td>
    </tr>
    <tr>
      <th>iAC560</th>
      <td>8.194865e-12</td>
      <td>9.868076e-12</td>
      <td>2.435742e-11</td>
      <td>8.923992e-12</td>
      <td>6.451882e-12</td>
      <td>7.145092e-12</td>
      <td>1.873765e-11</td>
      <td>1.947821e-11</td>
    </tr>
    <tr>
      <th>iAF1260</th>
      <td>1.781254e-09</td>
      <td>1.946048e-09</td>
      <td>5.678922e-09</td>
      <td>1.214388e-09</td>
      <td>8.198651e-10</td>
      <td>7.152690e-09</td>
      <td>9.012081e-09</td>
      <td>1.764879e-08</td>
    </tr>
    <tr>
      <th>iAF692</th>
      <td>3.386389e-09</td>
      <td>2.220311e-09</td>
      <td>8.946148e-09</td>
      <td>1.759396e-08</td>
      <td>1.963760e-09</td>
      <td>1.222407e-09</td>
      <td>8.575538e-09</td>
      <td>1.040327e-08</td>
    </tr>
    <tr>
      <th>iAI549</th>
      <td>1.612223e-11</td>
      <td>9.931913e-12</td>
      <td>4.028457e-11</td>
      <td>2.568619e-11</td>
      <td>1.368209e-11</td>
      <td>1.323319e-11</td>
      <td>1.541363e-11</td>
      <td>2.428250e-11</td>
    </tr>
    <tr>
      <th>iAN840m</th>
      <td>3.298200e-10</td>
      <td>1.804508e-10</td>
      <td>1.107875e-10</td>
      <td>2.751869e-10</td>
      <td>2.302759e-10</td>
      <td>2.859458e-10</td>
      <td>8.054293e-10</td>
      <td>1.172849e-09</td>
    </tr>
    <tr>
      <th>iAO358</th>
      <td>1.124310e-11</td>
      <td>1.091583e-11</td>
      <td>3.182512e-11</td>
      <td>1.906676e-11</td>
      <td>1.175427e-11</td>
      <td>1.348169e-11</td>
      <td>1.847833e-11</td>
      <td>2.943036e-11</td>
    </tr>
    <tr>
      <th>iAbaylyiV4</th>
      <td>2.977077e-12</td>
      <td>3.012134e-12</td>
      <td>8.290163e-12</td>
      <td>5.293440e-12</td>
      <td>6.227974e-12</td>
      <td>4.977532e-12</td>
      <td>1.004922e-11</td>
      <td>1.594689e-11</td>
    </tr>
    <tr>
      <th>iBT721_fixed</th>
      <td>6.197820e-12</td>
      <td>3.083755e-12</td>
      <td>4.031970e-11</td>
      <td>1.364242e-12</td>
      <td>2.629008e-12</td>
      <td>4.273915e-12</td>
      <td>3.751666e-12</td>
      <td>1.984154e-11</td>
    </tr>
    <tr>
      <th>iBsu1103</th>
      <td>2.972863e-10</td>
      <td>6.526051e-06</td>
      <td>7.303685e-10</td>
      <td>3.339946e-10</td>
      <td>2.010636e-10</td>
      <td>3.242728e-10</td>
      <td>5.418732e-10</td>
      <td>8.971953e-10</td>
    </tr>
    <tr>
      <th>iCA1273</th>
      <td>2.755569e-12</td>
      <td>2.649891e-12</td>
      <td>9.081865e-11</td>
      <td>2.677644e-12</td>
      <td>1.519041e-12</td>
      <td>3.057492e-12</td>
      <td>8.550924e-12</td>
      <td>1.762628e-11</td>
    </tr>
    <tr>
      <th>iCB925</th>
      <td>1.736274e-14</td>
      <td>9.613512e-15</td>
      <td>2.816809e-14</td>
      <td>1.165951e-14</td>
      <td>1.306301e-14</td>
      <td>2.114921e-14</td>
      <td>5.169930e-12</td>
      <td>1.014086e-11</td>
    </tr>
    <tr>
      <th>iCR744</th>
      <td>1.018664e-11</td>
      <td>6.352933e-12</td>
      <td>3.419470e-11</td>
      <td>1.823183e-11</td>
      <td>6.848318e-12</td>
      <td>6.607602e-12</td>
      <td>1.363850e-11</td>
      <td>1.417687e-11</td>
    </tr>
    <tr>
      <th>iCS291</th>
      <td>4.977130e-13</td>
      <td>3.683998e-13</td>
      <td>1.375014e-12</td>
      <td>8.569881e-13</td>
      <td>3.690381e-13</td>
      <td>3.893899e-13</td>
      <td>4.744788e-12</td>
      <td>6.790318e-12</td>
    </tr>
    <tr>
      <th>iCS400</th>
      <td>1.469269e-12</td>
      <td>1.157699e-12</td>
      <td>2.533241e-11</td>
      <td>1.845843e-12</td>
      <td>4.832384e-13</td>
      <td>1.527389e-12</td>
      <td>5.889844e-12</td>
      <td>9.199558e-12</td>
    </tr>
    <tr>
      <th>iCac802</th>
      <td>8.493680e-14</td>
      <td>3.153588e-14</td>
      <td>1.363077e-13</td>
      <td>1.898222e-13</td>
      <td>7.927829e-14</td>
      <td>7.058789e-14</td>
      <td>1.260632e-11</td>
      <td>1.055401e-11</td>
    </tr>
    <tr>
      <th>iFF708</th>
      <td>9.631808e-12</td>
      <td>5.780962e-12</td>
      <td>1.847612e-11</td>
      <td>6.812400e-12</td>
      <td>5.430347e-12</td>
      <td>1.020766e-11</td>
      <td>8.761480e-12</td>
      <td>2.012872e-11</td>
    </tr>
    <tr>
      <th>iGB555_fixed</th>
      <td>1.618755e-11</td>
      <td>4.991450e-10</td>
      <td>3.935196e-11</td>
      <td>8.029397e-12</td>
      <td>5.976067e-12</td>
      <td>1.892854e-11</td>
      <td>8.302095e-12</td>
      <td>3.028083e-11</td>
    </tr>
    <tr>
      <th>iHD666_fixed</th>
      <td>6.101243e-12</td>
      <td>2.778296e-11</td>
      <td>1.746997e-11</td>
      <td>3.751388e-12</td>
      <td>3.346992e-12</td>
      <td>7.398641e-12</td>
      <td>6.864509e-12</td>
      <td>1.167770e-11</td>
    </tr>
    <tr>
      <th>iIB711</th>
      <td>8.816919e-12</td>
      <td>9.826012e-12</td>
      <td>2.293666e-11</td>
      <td>2.186360e-11</td>
      <td>1.150156e-11</td>
      <td>1.309052e-11</td>
      <td>1.211514e-11</td>
      <td>2.583597e-11</td>
    </tr>
    <tr>
      <th>iIT341</th>
      <td>1.014080e-09</td>
      <td>1.807772e-09</td>
      <td>5.907021e-09</td>
      <td>8.119830e-10</td>
      <td>2.710340e-10</td>
      <td>1.470638e-09</td>
      <td>5.405914e-09</td>
      <td>7.601729e-09</td>
    </tr>
    <tr>
      <th>iJL432</th>
      <td>1.174412e-12</td>
      <td>3.901074e-13</td>
      <td>1.789826e-12</td>
      <td>3.963390e-13</td>
      <td>3.900797e-13</td>
      <td>7.603562e-13</td>
      <td>4.689371e-12</td>
      <td>3.737990e-12</td>
    </tr>
    <tr>
      <th>iJN678</th>
      <td>2.398464e-14</td>
      <td>2.797895e-10</td>
      <td>1.930007e-14</td>
      <td>1.396985e-14</td>
      <td>2.238604e-14</td>
      <td>2.488953e-14</td>
      <td>7.036177e-12</td>
      <td>5.716085e-12</td>
    </tr>
    <tr>
      <th>iJN746</th>
      <td>5.745402e-09</td>
      <td>1.309358e-08</td>
      <td>9.719125e-09</td>
      <td>3.280881e-09</td>
      <td>2.846633e-09</td>
      <td>4.145871e-09</td>
      <td>8.716805e-09</td>
      <td>1.037925e-08</td>
    </tr>
    <tr>
      <th>iJO1366</th>
      <td>3.229136e-12</td>
      <td>2.352308e-09</td>
      <td>1.235567e-11</td>
      <td>5.307026e-12</td>
      <td>8.026430e-13</td>
      <td>4.692354e-12</td>
      <td>9.259564e-12</td>
      <td>1.267621e-11</td>
    </tr>
    <tr>
      <th>iJP815</th>
      <td>1.020123e-09</td>
      <td>7.944625e-10</td>
      <td>3.420634e-09</td>
      <td>1.550045e-08</td>
      <td>7.528140e-10</td>
      <td>1.367096e-09</td>
      <td>1.359488e-08</td>
      <td>5.964099e-09</td>
    </tr>
    <tr>
      <th>iJR904</th>
      <td>1.099850e-09</td>
      <td>3.218263e-09</td>
      <td>4.340962e-09</td>
      <td>6.192079e-10</td>
      <td>1.427380e-10</td>
      <td>1.365733e-09</td>
      <td>6.213569e-09</td>
      <td>1.420731e-08</td>
    </tr>
    <tr>
      <th>iJS747</th>
      <td>7.176808e-12</td>
      <td>3.632675e-07</td>
      <td>9.697313e-12</td>
      <td>9.643009e-12</td>
      <td>3.800987e-12</td>
      <td>4.923902e-12</td>
      <td>5.578066e-12</td>
      <td>8.495003e-12</td>
    </tr>
    <tr>
      <th>iKF1028</th>
      <td>4.410775e-09</td>
      <td>2.512140e-09</td>
      <td>3.931006e-09</td>
      <td>4.556265e-09</td>
      <td>1.713361e-09</td>
      <td>4.626908e-09</td>
      <td>1.043391e-08</td>
      <td>1.115077e-08</td>
    </tr>
    <tr>
      <th>iLC915</th>
      <td>8.942108e-12</td>
      <td>5.859216e-12</td>
      <td>2.288417e-11</td>
      <td>9.887922e-12</td>
      <td>6.807457e-12</td>
      <td>1.100345e-11</td>
      <td>1.760760e-11</td>
      <td>1.649339e-11</td>
    </tr>
    <tr>
      <th>iLL672</th>
      <td>7.130910e-12</td>
      <td>7.483421e-09</td>
      <td>3.135656e-11</td>
      <td>7.181390e-12</td>
      <td>5.127530e-12</td>
      <td>1.080215e-11</td>
      <td>5.221250e-12</td>
      <td>1.864336e-11</td>
    </tr>
    <tr>
      <th>iMA871</th>
      <td>8.159995e-12</td>
      <td>4.129003e-12</td>
      <td>3.886357e-11</td>
      <td>9.557480e-12</td>
      <td>4.393495e-12</td>
      <td>7.955587e-12</td>
      <td>1.248793e-11</td>
      <td>2.376854e-11</td>
    </tr>
    <tr>
      <th>iMA945</th>
      <td>1.398577e-11</td>
      <td>1.241593e-11</td>
      <td>6.318794e-10</td>
      <td>1.253969e-11</td>
      <td>7.349408e-12</td>
      <td>9.134488e-12</td>
      <td>2.082624e-11</td>
      <td>1.493498e-11</td>
    </tr>
    <tr>
      <th>iMB745</th>
      <td>5.070478e-12</td>
      <td>4.316394e-12</td>
      <td>3.264610e-11</td>
      <td>6.657764e-12</td>
      <td>3.221213e-12</td>
      <td>5.698374e-12</td>
      <td>1.078196e-11</td>
      <td>1.047325e-10</td>
    </tr>
    <tr>
      <th>iMH551</th>
      <td>2.251095e-12</td>
      <td>1.368655e-12</td>
      <td>1.658942e-11</td>
      <td>1.702092e-12</td>
      <td>1.852061e-12</td>
      <td>2.130895e-12</td>
      <td>7.064203e-12</td>
      <td>1.524475e-11</td>
    </tr>
    <tr>
      <th>iMM1415</th>
      <td>1.248012e-09</td>
      <td>6.982713e-10</td>
      <td>3.418482e-09</td>
      <td>8.552331e-10</td>
      <td>6.642941e-10</td>
      <td>1.483438e-09</td>
      <td>2.067248e-09</td>
      <td>5.278308e-09</td>
    </tr>
    <tr>
      <th>iMM904</th>
      <td>3.595750e-09</td>
      <td>3.644007e-09</td>
      <td>8.308698e-09</td>
      <td>2.982506e-09</td>
      <td>1.531252e-09</td>
      <td>4.619449e-09</td>
      <td>7.938743e-09</td>
      <td>1.828506e-08</td>
    </tr>
    <tr>
      <th>iMO1056</th>
      <td>4.451167e-12</td>
      <td>4.065560e-09</td>
      <td>5.216133e-12</td>
      <td>2.091337e-12</td>
      <td>2.158161e-12</td>
      <td>4.592567e-12</td>
      <td>7.587645e-12</td>
      <td>1.088813e-11</td>
    </tr>
    <tr>
      <th>iMP429_fixed</th>
      <td>1.037411e-12</td>
      <td>6.876871e-13</td>
      <td>2.242258e-12</td>
      <td>5.857062e-13</td>
      <td>1.149136e-12</td>
      <td>1.776228e-12</td>
      <td>6.084059e-12</td>
      <td>9.247175e-12</td>
    </tr>
    <tr>
      <th>iND750</th>
      <td>2.859207e-09</td>
      <td>2.514810e-09</td>
      <td>5.778406e-09</td>
      <td>8.041428e-09</td>
      <td>2.058405e-09</td>
      <td>3.681656e-09</td>
      <td>7.571422e-09</td>
      <td>1.155155e-08</td>
    </tr>
    <tr>
      <th>iNJ661</th>
      <td>4.577143e-09</td>
      <td>4.961898e-09</td>
      <td>6.366734e-09</td>
      <td>3.712113e-09</td>
      <td>3.654260e-09</td>
      <td>4.502374e-09</td>
      <td>1.052895e-08</td>
      <td>1.091361e-08</td>
    </tr>
    <tr>
      <th>iNJ661m</th>
      <td>4.915935e-12</td>
      <td>1.054765e-11</td>
      <td>1.969559e-11</td>
      <td>1.044025e-07</td>
      <td>2.524202e-12</td>
      <td>5.219989e-07</td>
      <td>4.698032e-07</td>
      <td>1.416549e-11</td>
    </tr>
    <tr>
      <th>iNV213</th>
      <td>4.984638e-12</td>
      <td>2.831209e-07</td>
      <td>1.319748e-11</td>
      <td>4.020673e-12</td>
      <td>1.957150e-12</td>
      <td>3.845659e-12</td>
      <td>6.196237e-12</td>
      <td>8.082979e-12</td>
    </tr>
    <tr>
      <th>iOG654</th>
      <td>9.605928e-12</td>
      <td>6.018975e-12</td>
      <td>2.579665e-11</td>
      <td>6.017891e-12</td>
      <td>9.601608e-12</td>
      <td>1.360856e-11</td>
      <td>1.486815e-11</td>
      <td>2.803368e-11</td>
    </tr>
    <tr>
      <th>iOR363</th>
      <td>2.717474e-12</td>
      <td>0.000000e+00</td>
      <td>3.817827e-11</td>
      <td>2.046363e-12</td>
      <td>0.000000e+00</td>
      <td>4.687704e-12</td>
      <td>3.893774e-12</td>
      <td>4.926430e-12</td>
    </tr>
    <tr>
      <th>iPP668</th>
      <td>5.361779e-12</td>
      <td>2.598573e-12</td>
      <td>1.432983e-11</td>
      <td>1.154974e-12</td>
      <td>1.613025e-12</td>
      <td>4.027082e-12</td>
      <td>3.367375e-12</td>
      <td>1.306011e-11</td>
    </tr>
    <tr>
      <th>iPS189_fixed</th>
      <td>4.986594e-13</td>
      <td>2.228602e-09</td>
      <td>6.076497e-13</td>
      <td>6.313791e-13</td>
      <td>2.516057e-13</td>
      <td>8.629994e-13</td>
      <td>1.503601e-11</td>
      <td>3.438656e-12</td>
    </tr>
    <tr>
      <th>iRC1080</th>
      <td>1.212713e-11</td>
      <td>5.622330e-08</td>
      <td>2.998578e-11</td>
      <td>1.227949e-11</td>
      <td>5.134023e-12</td>
      <td>1.027390e-11</td>
      <td>3.109267e-11</td>
      <td>3.641264e-11</td>
    </tr>
    <tr>
      <th>iRM588</th>
      <td>4.377281e-10</td>
      <td>6.098593e-06</td>
      <td>9.950361e-10</td>
      <td>3.434693e-10</td>
      <td>2.256777e-10</td>
      <td>7.210925e-10</td>
      <td>8.615869e-10</td>
      <td>7.823844e-10</td>
    </tr>
    <tr>
      <th>iRR1083</th>
      <td>8.190296e-12</td>
      <td>1.242195e-06</td>
      <td>2.693539e-11</td>
      <td>1.105927e-11</td>
      <td>5.338382e-12</td>
      <td>9.888460e-12</td>
      <td>1.179566e-11</td>
      <td>1.757284e-11</td>
    </tr>
    <tr>
      <th>iRS1563</th>
      <td>2.844885e-12</td>
      <td>2.288953e-12</td>
      <td>1.005008e-11</td>
      <td>4.673761e-12</td>
      <td>1.709565e-12</td>
      <td>3.843955e-12</td>
      <td>1.646831e-11</td>
      <td>1.570177e-11</td>
    </tr>
    <tr>
      <th>iRS1597</th>
      <td>2.635014e-12</td>
      <td>3.367490e-12</td>
      <td>1.371104e-11</td>
      <td>3.210002e-12</td>
      <td>1.169068e-12</td>
      <td>1.140946e-12</td>
      <td>1.451179e-11</td>
      <td>5.307929e-12</td>
    </tr>
    <tr>
      <th>iRS605_fixed</th>
      <td>5.301002e-12</td>
      <td>5.221034e-12</td>
      <td>1.443769e-11</td>
      <td>8.543278e-12</td>
      <td>4.211766e-12</td>
      <td>4.851140e-12</td>
      <td>1.006191e-11</td>
      <td>1.255027e-11</td>
    </tr>
    <tr>
      <th>iRsp1095</th>
      <td>4.771094e-12</td>
      <td>1.286166e-07</td>
      <td>1.499878e-11</td>
      <td>5.990567e-12</td>
      <td>5.702781e-12</td>
      <td>5.757338e-12</td>
      <td>1.136189e-11</td>
      <td>3.360485e-11</td>
    </tr>
    <tr>
      <th>iSB619</th>
      <td>6.677286e-10</td>
      <td>2.461952e-10</td>
      <td>6.072867e-10</td>
      <td>2.292188e-11</td>
      <td>2.877589e-11</td>
      <td>1.436060e-10</td>
      <td>6.720453e-09</td>
      <td>1.817552e-08</td>
    </tr>
    <tr>
      <th>iSH335</th>
      <td>8.608735e-13</td>
      <td>7.918396e-13</td>
      <td>1.719772e-11</td>
      <td>2.412978e-13</td>
      <td>1.354082e-12</td>
      <td>7.116117e-13</td>
      <td>4.743332e-12</td>
      <td>5.824515e-12</td>
    </tr>
    <tr>
      <th>iSO783</th>
      <td>9.201850e-12</td>
      <td>2.860468e-10</td>
      <td>3.880035e-11</td>
      <td>2.266519e-11</td>
      <td>5.511215e-12</td>
      <td>1.131129e-11</td>
      <td>1.612790e-11</td>
      <td>1.880562e-11</td>
    </tr>
    <tr>
      <th>iSR432</th>
      <td>5.763678e-12</td>
      <td>2.818245e-07</td>
      <td>1.616559e-11</td>
      <td>5.417731e-12</td>
      <td>5.851002e-12</td>
      <td>4.656121e-12</td>
      <td>1.018306e-11</td>
      <td>1.522397e-11</td>
    </tr>
    <tr>
      <th>iSS724</th>
      <td>1.263471e-11</td>
      <td>1.255100e-11</td>
      <td>5.174531e-11</td>
      <td>1.577047e-11</td>
      <td>9.879180e-12</td>
      <td>1.510881e-11</td>
      <td>2.661788e-11</td>
      <td>4.044156e-10</td>
    </tr>
    <tr>
      <th>iSS884</th>
      <td>1.354254e-11</td>
      <td>9.174448e-12</td>
      <td>2.825013e-11</td>
      <td>6.639951e-12</td>
      <td>8.284437e-12</td>
      <td>9.998729e-12</td>
      <td>3.226585e-11</td>
      <td>2.586860e-11</td>
    </tr>
    <tr>
      <th>iSyn669</th>
      <td>8.127297e-11</td>
      <td>1.040794e-10</td>
      <td>1.415821e-10</td>
      <td>6.030044e-11</td>
      <td>2.003912e-11</td>
      <td>3.519071e-11</td>
      <td>1.160358e-10</td>
      <td>1.517444e-10</td>
    </tr>
    <tr>
      <th>iTH366</th>
      <td>4.467643e-09</td>
      <td>6.915386e-09</td>
      <td>1.450880e-08</td>
      <td>4.967946e-09</td>
      <td>4.431032e-09</td>
      <td>8.734066e-09</td>
      <td>1.281431e-08</td>
      <td>2.244135e-08</td>
    </tr>
    <tr>
      <th>iTL885</th>
      <td>7.174270e-12</td>
      <td>7.233351e-12</td>
      <td>1.081575e-11</td>
      <td>7.574101e-12</td>
      <td>2.522095e-12</td>
      <td>3.749231e-12</td>
      <td>9.384046e-12</td>
      <td>2.773719e-11</td>
    </tr>
    <tr>
      <th>iTY425_fixed</th>
      <td>1.357132e-12</td>
      <td>6.821528e-13</td>
      <td>3.765527e-12</td>
      <td>1.813959e-12</td>
      <td>9.112030e-13</td>
      <td>1.091689e-12</td>
      <td>5.685786e-12</td>
      <td>1.324586e-11</td>
    </tr>
    <tr>
      <th>iVM679</th>
      <td>5.441300e-12</td>
      <td>3.543573e-09</td>
      <td>1.112015e-11</td>
      <td>1.859461e-11</td>
      <td>2.503111e-12</td>
      <td>2.679210e-12</td>
      <td>1.226340e-11</td>
      <td>8.445926e-12</td>
    </tr>
    <tr>
      <th>iVS941_fixed</th>
      <td>5.781317e-12</td>
      <td>3.985063e-12</td>
      <td>2.889106e-11</td>
      <td>4.555880e-12</td>
      <td>4.109086e-12</td>
      <td>3.148214e-12</td>
      <td>8.170712e-12</td>
      <td>5.949118e-12</td>
    </tr>
    <tr>
      <th>iWV1314</th>
      <td>8.397096e-12</td>
      <td>9.542499e-12</td>
      <td>4.617399e-11</td>
      <td>1.552834e-11</td>
      <td>7.278331e-12</td>
      <td>9.208338e-12</td>
      <td>1.366008e-11</td>
      <td>1.755370e-11</td>
    </tr>
    <tr>
      <th>iWZ663</th>
      <td>7.253877e-12</td>
      <td>3.519589e-08</td>
      <td>4.027807e-11</td>
      <td>8.397005e-12</td>
      <td>5.308528e-12</td>
      <td>4.786052e-12</td>
      <td>1.215181e-11</td>
      <td>1.217298e-11</td>
    </tr>
    <tr>
      <th>iYL1228</th>
      <td>3.579303e-12</td>
      <td>5.812428e-10</td>
      <td>6.740615e-12</td>
      <td>1.638551e-12</td>
      <td>6.258599e-13</td>
      <td>1.245614e-12</td>
      <td>9.171871e-12</td>
      <td>1.130580e-11</td>
    </tr>
    <tr>
      <th>iYO844</th>
      <td>6.749347e-12</td>
      <td>1.459393e-08</td>
      <td>5.658764e-12</td>
      <td>1.799575e-12</td>
      <td>1.478164e-12</td>
      <td>1.119653e-12</td>
      <td>6.888139e-12</td>
      <td>2.063596e-11</td>
    </tr>
    <tr>
      <th>iZM363</th>
      <td>5.369345e-12</td>
      <td>5.353776e-12</td>
      <td>1.529245e-11</td>
      <td>7.623997e-12</td>
      <td>4.478320e-12</td>
      <td>5.519462e-12</td>
      <td>8.284732e-12</td>
      <td>1.405405e-11</td>
    </tr>
    <tr>
      <th>iZmobMBEL601</th>
      <td>1.672617e-12</td>
      <td>1.524215e-12</td>
      <td>4.595579e-12</td>
      <td>2.783999e-12</td>
      <td>4.085307e-13</td>
      <td>1.355290e-12</td>
      <td>6.795329e-12</td>
      <td>6.571501e-12</td>
    </tr>
    <tr>
      <th>mus_musculus</th>
      <td>9.798615e-12</td>
      <td>4.947154e-12</td>
      <td>2.169150e-11</td>
      <td>6.331269e-12</td>
      <td>4.835687e-12</td>
      <td>8.265638e-12</td>
      <td>1.813938e-11</td>
      <td>1.927275e-11</td>
    </tr>
    <tr>
      <th>textbook</th>
      <td>7.371881e-14</td>
      <td>2.203700e-09</td>
      <td>2.109380e-13</td>
      <td>5.417888e-14</td>
      <td>4.862777e-14</td>
      <td>8.348877e-14</td>
      <td>1.268388e-09</td>
      <td>2.745516e-09</td>
    </tr>
  </tbody>
</table>
</div>



Here are all the computed biomass flux rates for each solver and model.


```python
results.T
```




<div>
<table border="1" class="dataframe">
  <thead>
    <tr style="text-align: right;">
      <th></th>
      <th>cglpk</th>
      <th>cglpk_exact</th>
      <th>coin</th>
      <th>cplex</th>
      <th>esolver</th>
      <th>glpk</th>
      <th>gurobi</th>
      <th>mosek</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <th>AbyMBEL891</th>
      <td>119.233012</td>
      <td>119.233012</td>
      <td>119.233012</td>
      <td>119.233012</td>
      <td>119.233012</td>
      <td>119.233012</td>
      <td>119.233012</td>
      <td>119.233012</td>
    </tr>
    <tr>
      <th>AraGEM</th>
      <td>10.000000</td>
      <td>10.000000</td>
      <td>10.000000</td>
      <td>10.000000</td>
      <td>10.000000</td>
      <td>10.000000</td>
      <td>10.000000</td>
      <td>10.000000</td>
    </tr>
    <tr>
      <th>GSMN_TB</th>
      <td>0.131262</td>
      <td>0.131262</td>
      <td>0.131262</td>
      <td>0.131262</td>
      <td>0.131262</td>
      <td>0.131262</td>
      <td>0.131262</td>
      <td>0.131262</td>
    </tr>
    <tr>
      <th>PpaMBEL1254</th>
      <td>78.700594</td>
      <td>78.700594</td>
      <td>78.700594</td>
      <td>78.700594</td>
      <td>78.700594</td>
      <td>78.700594</td>
      <td>78.700594</td>
      <td>78.700594</td>
    </tr>
    <tr>
      <th>PpuMBEL1071</th>
      <td>132.365353</td>
      <td>132.365353</td>
      <td>132.365353</td>
      <td>132.365353</td>
      <td>132.365353</td>
      <td>132.365353</td>
      <td>132.365353</td>
      <td>132.365353</td>
    </tr>
    <tr>
      <th>STM_v1_0</th>
      <td>0.477834</td>
      <td>0.477834</td>
      <td>0.477834</td>
      <td>0.477834</td>
      <td>0.477834</td>
      <td>0.477834</td>
      <td>0.477834</td>
      <td>0.477834</td>
    </tr>
    <tr>
      <th>S_coilicolor_fixed</th>
      <td>860.088835</td>
      <td>860.088835</td>
      <td>860.088835</td>
      <td>860.088835</td>
      <td>860.088835</td>
      <td>860.088835</td>
      <td>860.088835</td>
      <td>860.088835</td>
    </tr>
    <tr>
      <th>SpoMBEL1693</th>
      <td>63.785658</td>
      <td>63.785658</td>
      <td>63.785658</td>
      <td>63.785658</td>
      <td>63.785658</td>
      <td>63.785658</td>
      <td>63.785658</td>
      <td>63.785658</td>
    </tr>
    <tr>
      <th>T_Maritima</th>
      <td>0.359469</td>
      <td>0.359469</td>
      <td>0.359469</td>
      <td>0.359469</td>
      <td>0.359469</td>
      <td>0.359469</td>
      <td>0.359469</td>
      <td>0.359469</td>
    </tr>
    <tr>
      <th>VvuMBEL943</th>
      <td>96.402322</td>
      <td>96.402322</td>
      <td>96.402322</td>
      <td>96.402322</td>
      <td>96.402322</td>
      <td>96.402322</td>
      <td>96.402322</td>
      <td>96.402322</td>
    </tr>
    <tr>
      <th>iAC560</th>
      <td>4.042612</td>
      <td>4.042612</td>
      <td>4.042612</td>
      <td>4.042612</td>
      <td>4.042612</td>
      <td>4.042612</td>
      <td>4.042612</td>
      <td>4.042612</td>
    </tr>
    <tr>
      <th>iAF1260</th>
      <td>0.736701</td>
      <td>0.736701</td>
      <td>0.736701</td>
      <td>0.736701</td>
      <td>0.736701</td>
      <td>0.736701</td>
      <td>0.736701</td>
      <td>0.736701</td>
    </tr>
    <tr>
      <th>iAF692</th>
      <td>0.027250</td>
      <td>0.027250</td>
      <td>0.027250</td>
      <td>0.027250</td>
      <td>0.027250</td>
      <td>0.027250</td>
      <td>0.027250</td>
      <td>0.027250</td>
    </tr>
    <tr>
      <th>iAI549</th>
      <td>84.174193</td>
      <td>84.174193</td>
      <td>84.174193</td>
      <td>84.174193</td>
      <td>84.174193</td>
      <td>84.174193</td>
      <td>84.174193</td>
      <td>84.174193</td>
    </tr>
    <tr>
      <th>iAN840m</th>
      <td>0.340136</td>
      <td>0.340136</td>
      <td>0.340136</td>
      <td>0.340136</td>
      <td>0.340136</td>
      <td>0.340136</td>
      <td>0.340136</td>
      <td>0.340136</td>
    </tr>
    <tr>
      <th>iAO358</th>
      <td>255.180548</td>
      <td>255.180548</td>
      <td>255.180548</td>
      <td>255.180548</td>
      <td>255.180548</td>
      <td>255.180548</td>
      <td>255.180548</td>
      <td>255.180548</td>
    </tr>
    <tr>
      <th>iAbaylyiV4</th>
      <td>12.306545</td>
      <td>12.306545</td>
      <td>12.306545</td>
      <td>12.306545</td>
      <td>12.306545</td>
      <td>12.306545</td>
      <td>12.306545</td>
      <td>12.306545</td>
    </tr>
    <tr>
      <th>iBT721_fixed</th>
      <td>0.500000</td>
      <td>0.500000</td>
      <td>0.500000</td>
      <td>0.500000</td>
      <td>0.500000</td>
      <td>0.500000</td>
      <td>0.500000</td>
      <td>0.500000</td>
    </tr>
    <tr>
      <th>iBsu1103</th>
      <td>1229.657244</td>
      <td>1229.657244</td>
      <td>1229.657244</td>
      <td>1229.657244</td>
      <td>1229.657244</td>
      <td>1229.657244</td>
      <td>1229.657244</td>
      <td>1229.657244</td>
    </tr>
    <tr>
      <th>iCA1273</th>
      <td>0.740242</td>
      <td>0.740242</td>
      <td>0.740242</td>
      <td>0.740242</td>
      <td>0.740242</td>
      <td>0.740242</td>
      <td>0.740242</td>
      <td>0.740242</td>
    </tr>
    <tr>
      <th>iCB925</th>
      <td>0.119428</td>
      <td>0.119428</td>
      <td>0.119428</td>
      <td>0.119428</td>
      <td>0.119428</td>
      <td>0.119428</td>
      <td>0.119428</td>
      <td>0.119428</td>
    </tr>
    <tr>
      <th>iCR744</th>
      <td>41.476742</td>
      <td>41.476742</td>
      <td>41.476742</td>
      <td>41.476742</td>
      <td>41.476742</td>
      <td>41.476742</td>
      <td>41.476742</td>
      <td>41.476742</td>
    </tr>
    <tr>
      <th>iCS291</th>
      <td>0.140549</td>
      <td>0.140549</td>
      <td>0.140549</td>
      <td>0.140549</td>
      <td>0.140549</td>
      <td>0.140549</td>
      <td>0.140549</td>
      <td>0.140549</td>
    </tr>
    <tr>
      <th>iCS400</th>
      <td>0.215639</td>
      <td>0.215639</td>
      <td>0.215639</td>
      <td>0.215639</td>
      <td>0.215639</td>
      <td>0.215639</td>
      <td>0.215639</td>
      <td>0.215639</td>
    </tr>
    <tr>
      <th>iCac802</th>
      <td>0.209597</td>
      <td>0.209597</td>
      <td>0.209597</td>
      <td>0.209597</td>
      <td>0.209597</td>
      <td>0.209597</td>
      <td>0.209597</td>
      <td>0.209597</td>
    </tr>
    <tr>
      <th>iFF708</th>
      <td>14.917106</td>
      <td>14.917106</td>
      <td>14.917106</td>
      <td>14.917106</td>
      <td>14.917106</td>
      <td>14.917106</td>
      <td>14.917106</td>
      <td>14.917106</td>
    </tr>
    <tr>
      <th>iGB555_fixed</th>
      <td>127.789084</td>
      <td>127.789084</td>
      <td>127.789084</td>
      <td>127.789084</td>
      <td>127.789084</td>
      <td>127.789084</td>
      <td>127.789084</td>
      <td>127.789084</td>
    </tr>
    <tr>
      <th>iHD666_fixed</th>
      <td>0.255672</td>
      <td>0.255672</td>
      <td>0.255672</td>
      <td>0.255672</td>
      <td>0.255672</td>
      <td>0.255672</td>
      <td>0.255672</td>
      <td>0.255672</td>
    </tr>
    <tr>
      <th>iIB711</th>
      <td>84.688415</td>
      <td>84.688415</td>
      <td>84.688415</td>
      <td>84.688415</td>
      <td>84.688415</td>
      <td>84.688415</td>
      <td>84.688415</td>
      <td>84.688415</td>
    </tr>
    <tr>
      <th>iIT341</th>
      <td>0.692813</td>
      <td>0.692813</td>
      <td>0.692813</td>
      <td>0.692813</td>
      <td>0.692813</td>
      <td>0.692813</td>
      <td>0.692813</td>
      <td>0.692813</td>
    </tr>
    <tr>
      <th>iJL432</th>
      <td>0.328741</td>
      <td>0.328741</td>
      <td>0.328741</td>
      <td>0.328741</td>
      <td>0.328741</td>
      <td>0.328741</td>
      <td>0.328741</td>
      <td>0.328741</td>
    </tr>
    <tr>
      <th>iJN678</th>
      <td>0.063150</td>
      <td>0.063150</td>
      <td>0.063150</td>
      <td>0.063150</td>
      <td>0.063150</td>
      <td>0.063150</td>
      <td>0.063150</td>
      <td>0.063150</td>
    </tr>
    <tr>
      <th>iJN746</th>
      <td>3.679412</td>
      <td>3.679412</td>
      <td>3.679412</td>
      <td>3.679412</td>
      <td>3.679412</td>
      <td>3.679412</td>
      <td>3.679412</td>
      <td>3.679412</td>
    </tr>
    <tr>
      <th>iJO1366</th>
      <td>0.982372</td>
      <td>0.982372</td>
      <td>0.982372</td>
      <td>0.982372</td>
      <td>0.982372</td>
      <td>0.982372</td>
      <td>0.982372</td>
      <td>0.982372</td>
    </tr>
    <tr>
      <th>iJP815</th>
      <td>0.861512</td>
      <td>0.861512</td>
      <td>0.861512</td>
      <td>0.861512</td>
      <td>0.861512</td>
      <td>0.861512</td>
      <td>0.861512</td>
      <td>0.861512</td>
    </tr>
    <tr>
      <th>iJR904</th>
      <td>0.921948</td>
      <td>0.921948</td>
      <td>0.921948</td>
      <td>0.921948</td>
      <td>0.921948</td>
      <td>0.921948</td>
      <td>0.921948</td>
      <td>0.921948</td>
    </tr>
    <tr>
      <th>iJS747</th>
      <td>34.172662</td>
      <td>34.172662</td>
      <td>34.172662</td>
      <td>34.172662</td>
      <td>34.172662</td>
      <td>34.172662</td>
      <td>34.172662</td>
      <td>34.172662</td>
    </tr>
    <tr>
      <th>iKF1028</th>
      <td>0.517807</td>
      <td>0.517807</td>
      <td>0.517807</td>
      <td>0.517807</td>
      <td>0.517807</td>
      <td>0.517807</td>
      <td>0.517807</td>
      <td>0.517807</td>
    </tr>
    <tr>
      <th>iLC915</th>
      <td>79.021232</td>
      <td>79.021232</td>
      <td>79.021232</td>
      <td>79.021232</td>
      <td>79.021232</td>
      <td>79.021232</td>
      <td>79.021232</td>
      <td>79.021232</td>
    </tr>
    <tr>
      <th>iLL672</th>
      <td>3.475283</td>
      <td>3.475283</td>
      <td>3.475283</td>
      <td>3.475283</td>
      <td>3.475283</td>
      <td>3.475283</td>
      <td>3.475283</td>
      <td>3.475283</td>
    </tr>
    <tr>
      <th>iMA871</th>
      <td>27.792976</td>
      <td>27.792976</td>
      <td>27.792976</td>
      <td>27.792976</td>
      <td>27.792976</td>
      <td>27.792976</td>
      <td>27.792976</td>
      <td>27.792976</td>
    </tr>
    <tr>
      <th>iMA945</th>
      <td>79.589584</td>
      <td>79.589584</td>
      <td>79.589584</td>
      <td>79.589584</td>
      <td>79.589584</td>
      <td>79.589584</td>
      <td>79.589584</td>
      <td>79.589584</td>
    </tr>
    <tr>
      <th>iMB745</th>
      <td>0.030942</td>
      <td>0.030942</td>
      <td>0.030942</td>
      <td>0.030942</td>
      <td>0.030942</td>
      <td>0.030942</td>
      <td>0.030942</td>
      <td>0.030942</td>
    </tr>
    <tr>
      <th>iMH551</th>
      <td>0.775081</td>
      <td>0.775081</td>
      <td>0.775081</td>
      <td>0.775081</td>
      <td>0.775081</td>
      <td>0.775081</td>
      <td>0.775081</td>
      <td>0.775081</td>
    </tr>
    <tr>
      <th>iMM1415</th>
      <td>1.363428</td>
      <td>1.363428</td>
      <td>1.363428</td>
      <td>1.363428</td>
      <td>1.363428</td>
      <td>1.363428</td>
      <td>1.363428</td>
      <td>1.363428</td>
    </tr>
    <tr>
      <th>iMM904</th>
      <td>0.287866</td>
      <td>0.287866</td>
      <td>0.287866</td>
      <td>0.287866</td>
      <td>0.287866</td>
      <td>0.287866</td>
      <td>0.287866</td>
      <td>0.287866</td>
    </tr>
    <tr>
      <th>iMO1056</th>
      <td>1.047929</td>
      <td>1.047929</td>
      <td>1.047929</td>
      <td>1.047929</td>
      <td>1.047929</td>
      <td>1.047929</td>
      <td>1.047929</td>
      <td>1.047929</td>
    </tr>
    <tr>
      <th>iMP429_fixed</th>
      <td>0.804432</td>
      <td>0.804432</td>
      <td>0.804432</td>
      <td>0.804432</td>
      <td>0.804432</td>
      <td>0.804432</td>
      <td>0.804432</td>
      <td>0.804432</td>
    </tr>
    <tr>
      <th>iND750</th>
      <td>0.097323</td>
      <td>0.097323</td>
      <td>0.097323</td>
      <td>0.097323</td>
      <td>0.097323</td>
      <td>0.097323</td>
      <td>0.097323</td>
      <td>0.097323</td>
    </tr>
    <tr>
      <th>iNJ661</th>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
    </tr>
    <tr>
      <th>iNJ661m</th>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
      <td>0.052199</td>
    </tr>
    <tr>
      <th>iNV213</th>
      <td>11.538859</td>
      <td>11.538859</td>
      <td>11.538859</td>
      <td>11.538859</td>
      <td>11.538859</td>
      <td>11.538859</td>
      <td>11.538859</td>
      <td>11.538859</td>
    </tr>
    <tr>
      <th>iOG654</th>
      <td>0.355447</td>
      <td>0.355447</td>
      <td>0.355447</td>
      <td>0.355447</td>
      <td>0.355447</td>
      <td>0.355447</td>
      <td>0.355447</td>
      <td>0.355447</td>
    </tr>
    <tr>
      <th>iOR363</th>
      <td>250.000000</td>
      <td>250.000000</td>
      <td>250.000000</td>
      <td>250.000000</td>
      <td>250.000000</td>
      <td>250.000000</td>
      <td>250.000000</td>
      <td>250.000000</td>
    </tr>
    <tr>
      <th>iPP668</th>
      <td>3.891474</td>
      <td>3.891474</td>
      <td>3.891474</td>
      <td>3.891474</td>
      <td>3.891474</td>
      <td>3.891474</td>
      <td>3.891474</td>
      <td>3.891474</td>
    </tr>
    <tr>
      <th>iPS189_fixed</th>
      <td>2.238961</td>
      <td>2.238961</td>
      <td>2.238961</td>
      <td>2.238961</td>
      <td>2.238961</td>
      <td>2.238961</td>
      <td>2.238961</td>
      <td>2.238961</td>
    </tr>
    <tr>
      <th>iRC1080</th>
      <td>6.156851</td>
      <td>6.156851</td>
      <td>6.156851</td>
      <td>6.156851</td>
      <td>6.156851</td>
      <td>6.156851</td>
      <td>6.156851</td>
      <td>6.156851</td>
    </tr>
    <tr>
      <th>iRM588</th>
      <td>1000.000000</td>
      <td>1000.000000</td>
      <td>1000.000000</td>
      <td>1000.000000</td>
      <td>1000.000000</td>
      <td>1000.000000</td>
      <td>1000.000000</td>
      <td>1000.000000</td>
    </tr>
    <tr>
      <th>iRR1083</th>
      <td>77.947363</td>
      <td>77.947363</td>
      <td>77.947363</td>
      <td>77.947363</td>
      <td>77.947363</td>
      <td>77.947363</td>
      <td>77.947363</td>
      <td>77.947363</td>
    </tr>
    <tr>
      <th>iRS1563</th>
      <td>0.079962</td>
      <td>0.079962</td>
      <td>0.079962</td>
      <td>0.079962</td>
      <td>0.079962</td>
      <td>0.079962</td>
      <td>0.079962</td>
      <td>0.079962</td>
    </tr>
    <tr>
      <th>iRS1597</th>
      <td>8.969346</td>
      <td>8.969346</td>
      <td>8.969346</td>
      <td>8.969346</td>
      <td>8.969346</td>
      <td>8.969346</td>
      <td>8.969346</td>
      <td>8.969346</td>
    </tr>
    <tr>
      <th>iRS605_fixed</th>
      <td>2.116780</td>
      <td>2.116780</td>
      <td>2.116780</td>
      <td>2.116780</td>
      <td>2.116780</td>
      <td>2.116780</td>
      <td>2.116780</td>
      <td>2.116780</td>
    </tr>
    <tr>
      <th>iRsp1095</th>
      <td>9.686899</td>
      <td>9.686899</td>
      <td>9.686899</td>
      <td>9.686899</td>
      <td>9.686899</td>
      <td>9.686899</td>
      <td>9.686899</td>
      <td>9.686899</td>
    </tr>
    <tr>
      <th>iSB619</th>
      <td>0.158050</td>
      <td>0.158050</td>
      <td>0.158050</td>
      <td>0.158050</td>
      <td>0.158050</td>
      <td>0.158050</td>
      <td>0.158050</td>
      <td>0.158050</td>
    </tr>
    <tr>
      <th>iSH335</th>
      <td>1.159211</td>
      <td>1.159211</td>
      <td>1.159211</td>
      <td>1.159211</td>
      <td>1.159211</td>
      <td>1.159211</td>
      <td>1.159211</td>
      <td>1.159211</td>
    </tr>
    <tr>
      <th>iSO783</th>
      <td>17.920308</td>
      <td>17.920308</td>
      <td>17.920308</td>
      <td>17.920308</td>
      <td>17.920308</td>
      <td>17.920308</td>
      <td>17.920308</td>
      <td>17.920308</td>
    </tr>
    <tr>
      <th>iSR432</th>
      <td>11.482570</td>
      <td>11.482570</td>
      <td>11.482570</td>
      <td>11.482570</td>
      <td>11.482570</td>
      <td>11.482570</td>
      <td>11.482570</td>
      <td>11.482570</td>
    </tr>
    <tr>
      <th>iSS724</th>
      <td>22.421525</td>
      <td>22.421525</td>
      <td>22.421525</td>
      <td>22.421525</td>
      <td>22.421525</td>
      <td>22.421525</td>
      <td>22.421525</td>
      <td>22.421525</td>
    </tr>
    <tr>
      <th>iSS884</th>
      <td>70.359286</td>
      <td>70.359286</td>
      <td>70.359286</td>
      <td>70.359286</td>
      <td>70.359286</td>
      <td>70.359286</td>
      <td>70.359286</td>
      <td>70.359286</td>
    </tr>
    <tr>
      <th>iSyn669</th>
      <td>0.179090</td>
      <td>0.179090</td>
      <td>0.179090</td>
      <td>0.179090</td>
      <td>0.179090</td>
      <td>0.179090</td>
      <td>0.179090</td>
      <td>0.179090</td>
    </tr>
    <tr>
      <th>iTH366</th>
      <td>27890.888638</td>
      <td>27890.888638</td>
      <td>27890.888638</td>
      <td>27890.888638</td>
      <td>27890.888638</td>
      <td>27890.888638</td>
      <td>27890.888638</td>
      <td>27890.888638</td>
    </tr>
    <tr>
      <th>iTL885</th>
      <td>7.098836</td>
      <td>7.098836</td>
      <td>7.098836</td>
      <td>7.098836</td>
      <td>7.098836</td>
      <td>7.098836</td>
      <td>7.098836</td>
      <td>7.098836</td>
    </tr>
    <tr>
      <th>iTY425_fixed</th>
      <td>0.886833</td>
      <td>0.886833</td>
      <td>0.886833</td>
      <td>0.886833</td>
      <td>0.886833</td>
      <td>0.886833</td>
      <td>0.886833</td>
      <td>0.886833</td>
    </tr>
    <tr>
      <th>iVM679</th>
      <td>2.826570</td>
      <td>2.826570</td>
      <td>2.826570</td>
      <td>2.826570</td>
      <td>2.826570</td>
      <td>2.826570</td>
      <td>2.826570</td>
      <td>2.826570</td>
    </tr>
    <tr>
      <th>iVS941_fixed</th>
      <td>0.523385</td>
      <td>0.523385</td>
      <td>0.523385</td>
      <td>0.523385</td>
      <td>0.523385</td>
      <td>0.523385</td>
      <td>0.523385</td>
      <td>0.523385</td>
    </tr>
    <tr>
      <th>iWV1314</th>
      <td>25.682402</td>
      <td>25.682402</td>
      <td>25.682402</td>
      <td>25.682402</td>
      <td>25.682402</td>
      <td>25.682402</td>
      <td>25.682402</td>
      <td>25.682402</td>
    </tr>
    <tr>
      <th>iWZ663</th>
      <td>34.075881</td>
      <td>34.075881</td>
      <td>34.075881</td>
      <td>34.075881</td>
      <td>34.075881</td>
      <td>34.075881</td>
      <td>34.075881</td>
      <td>34.075881</td>
    </tr>
    <tr>
      <th>iYL1228</th>
      <td>1.042637</td>
      <td>1.042637</td>
      <td>1.042638</td>
      <td>1.042637</td>
      <td>1.042637</td>
      <td>1.042637</td>
      <td>1.042637</td>
      <td>1.042637</td>
    </tr>
    <tr>
      <th>iYO844</th>
      <td>1.582798</td>
      <td>1.582798</td>
      <td>1.582798</td>
      <td>1.582798</td>
      <td>1.582798</td>
      <td>1.582798</td>
      <td>1.582798</td>
      <td>1.582798</td>
    </tr>
    <tr>
      <th>iZM363</th>
      <td>2.532606</td>
      <td>2.532606</td>
      <td>2.532606</td>
      <td>2.532606</td>
      <td>2.532606</td>
      <td>2.532606</td>
      <td>2.532606</td>
      <td>2.532606</td>
    </tr>
    <tr>
      <th>iZmobMBEL601</th>
      <td>0.350080</td>
      <td>0.350080</td>
      <td>0.350080</td>
      <td>0.350080</td>
      <td>0.350080</td>
      <td>0.350080</td>
      <td>0.350080</td>
      <td>0.350080</td>
    </tr>
    <tr>
      <th>mus_musculus</th>
      <td>129.100556</td>
      <td>129.100556</td>
      <td>129.100556</td>
      <td>129.100556</td>
      <td>129.100556</td>
      <td>129.100556</td>
      <td>129.100556</td>
      <td>129.100556</td>
    </tr>
    <tr>
      <th>textbook</th>
      <td>0.873922</td>
      <td>0.873922</td>
      <td>0.873922</td>
      <td>0.873922</td>
      <td>0.873922</td>
      <td>0.873922</td>
      <td>0.873922</td>
      <td>0.873922</td>
    </tr>
  </tbody>
</table>
</div>



The objectives computed for these solvers are effectively the same as those computed by esolver.


```python
differences = (results - results.ix["esolver"]).T
differences.pop("esolver")
differences
```




<div>
<table border="1" class="dataframe">
  <thead>
    <tr style="text-align: right;">
      <th></th>
      <th>cglpk</th>
      <th>cglpk_exact</th>
      <th>coin</th>
      <th>cplex</th>
      <th>glpk</th>
      <th>gurobi</th>
      <th>mosek</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <th>AbyMBEL891</th>
      <td>1.136868e-13</td>
      <td>0.000000e+00</td>
      <td>3.844036e-11</td>
      <td>-5.684342e-14</td>
      <td>1.136868e-13</td>
      <td>-2.415845e-13</td>
      <td>9.947598e-14</td>
    </tr>
    <tr>
      <th>AraGEM</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
    </tr>
    <tr>
      <th>GSMN_TB</th>
      <td>-4.656553e-13</td>
      <td>0.000000e+00</td>
      <td>5.085987e-12</td>
      <td>-2.345454e-11</td>
      <td>1.011393e-08</td>
      <td>-1.665335e-15</td>
      <td>-1.402767e-12</td>
    </tr>
    <tr>
      <th>PpaMBEL1254</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>5.805134e-11</td>
      <td>-1.847411e-13</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>-7.105427e-14</td>
    </tr>
    <tr>
      <th>PpuMBEL1071</th>
      <td>8.526513e-14</td>
      <td>5.117897e-10</td>
      <td>4.602612e-10</td>
      <td>5.684342e-14</td>
      <td>8.526513e-14</td>
      <td>5.684342e-14</td>
      <td>-1.136868e-13</td>
    </tr>
    <tr>
      <th>STM_v1_0</th>
      <td>3.863576e-14</td>
      <td>4.957084e-10</td>
      <td>3.605212e-07</td>
      <td>-1.498801e-15</td>
      <td>1.086908e-13</td>
      <td>-4.996004e-16</td>
      <td>4.814482e-13</td>
    </tr>
    <tr>
      <th>S_coilicolor_fixed</th>
      <td>1.136868e-13</td>
      <td>0.000000e+00</td>
      <td>1.364242e-12</td>
      <td>0.000000e+00</td>
      <td>1.136868e-13</td>
      <td>0.000000e+00</td>
      <td>-1.250555e-12</td>
    </tr>
    <tr>
      <th>SpoMBEL1693</th>
      <td>-1.421085e-14</td>
      <td>0.000000e+00</td>
      <td>2.098943e-11</td>
      <td>-1.421085e-14</td>
      <td>7.105427e-14</td>
      <td>-2.842171e-14</td>
      <td>-6.039613e-13</td>
    </tr>
    <tr>
      <th>T_Maritima</th>
      <td>-3.214096e-14</td>
      <td>9.456913e-11</td>
      <td>2.230516e-09</td>
      <td>3.330669e-16</td>
      <td>-2.114975e-14</td>
      <td>-3.330669e-16</td>
      <td>8.437695e-14</td>
    </tr>
    <tr>
      <th>VvuMBEL943</th>
      <td>1.421085e-14</td>
      <td>0.000000e+00</td>
      <td>1.922729e-11</td>
      <td>4.263256e-14</td>
      <td>4.263256e-14</td>
      <td>0.000000e+00</td>
      <td>1.563194e-13</td>
    </tr>
    <tr>
      <th>iAC560</th>
      <td>2.664535e-15</td>
      <td>0.000000e+00</td>
      <td>8.553158e-13</td>
      <td>8.881784e-16</td>
      <td>0.000000e+00</td>
      <td>1.776357e-15</td>
      <td>1.421085e-14</td>
    </tr>
    <tr>
      <th>iAF1260</th>
      <td>2.087197e-11</td>
      <td>0.000000e+00</td>
      <td>8.428154e-08</td>
      <td>-2.066280e-11</td>
      <td>1.858336e-11</td>
      <td>-1.196998e-11</td>
      <td>1.749767e-11</td>
    </tr>
    <tr>
      <th>iAF692</th>
      <td>-3.651770e-11</td>
      <td>-2.846202e-11</td>
      <td>1.981591e-09</td>
      <td>6.965345e-09</td>
      <td>-4.769716e-12</td>
      <td>2.617935e-09</td>
      <td>-1.106832e-09</td>
    </tr>
    <tr>
      <th>iAI549</th>
      <td>-7.673862e-13</td>
      <td>0.000000e+00</td>
      <td>5.840661e-11</td>
      <td>-5.826450e-13</td>
      <td>1.705303e-13</td>
      <td>-1.236344e-12</td>
      <td>6.963319e-13</td>
    </tr>
    <tr>
      <th>iAN840m</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>1.872813e-08</td>
      <td>-5.551115e-17</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
    </tr>
    <tr>
      <th>iAO358</th>
      <td>-8.526513e-14</td>
      <td>0.000000e+00</td>
      <td>1.497824e-11</td>
      <td>-1.989520e-13</td>
      <td>2.842171e-14</td>
      <td>-5.115908e-13</td>
      <td>-5.684342e-14</td>
    </tr>
    <tr>
      <th>iAbaylyiV4</th>
      <td>4.796163e-14</td>
      <td>-1.776357e-15</td>
      <td>8.941647e-11</td>
      <td>-1.776357e-15</td>
      <td>1.953993e-14</td>
      <td>1.065814e-14</td>
      <td>-4.494183e-13</td>
    </tr>
    <tr>
      <th>iBT721_fixed</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>-6.938894e-15</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>1.110223e-16</td>
    </tr>
    <tr>
      <th>iBsu1103</th>
      <td>-2.273737e-13</td>
      <td>-2.653928e-08</td>
      <td>5.934453e-11</td>
      <td>-1.136868e-12</td>
      <td>2.273737e-13</td>
      <td>0.000000e+00</td>
      <td>2.046363e-12</td>
    </tr>
    <tr>
      <th>iCA1273</th>
      <td>-3.275158e-14</td>
      <td>0.000000e+00</td>
      <td>1.637933e-08</td>
      <td>4.685141e-14</td>
      <td>5.406786e-14</td>
      <td>-4.696243e-14</td>
      <td>2.265965e-13</td>
    </tr>
    <tr>
      <th>iCB925</th>
      <td>7.494005e-16</td>
      <td>0.000000e+00</td>
      <td>2.920300e-11</td>
      <td>-3.191891e-16</td>
      <td>-1.942890e-16</td>
      <td>2.636780e-16</td>
      <td>-2.703671e-13</td>
    </tr>
    <tr>
      <th>iCR744</th>
      <td>3.552714e-14</td>
      <td>0.000000e+00</td>
      <td>2.358817e-09</td>
      <td>-5.826450e-13</td>
      <td>-1.350031e-13</td>
      <td>1.705303e-13</td>
      <td>5.186962e-13</td>
    </tr>
    <tr>
      <th>iCS291</th>
      <td>1.193490e-15</td>
      <td>0.000000e+00</td>
      <td>2.731065e-12</td>
      <td>-6.938894e-16</td>
      <td>-1.110223e-15</td>
      <td>-1.276756e-15</td>
      <td>-3.608225e-16</td>
    </tr>
    <tr>
      <th>iCS400</th>
      <td>-1.026956e-15</td>
      <td>0.000000e+00</td>
      <td>4.090339e-13</td>
      <td>-1.110223e-16</td>
      <td>2.470246e-15</td>
      <td>0.000000e+00</td>
      <td>1.956768e-14</td>
    </tr>
    <tr>
      <th>iCac802</th>
      <td>4.440892e-16</td>
      <td>0.000000e+00</td>
      <td>9.617439e-09</td>
      <td>-1.665335e-16</td>
      <td>-1.249001e-15</td>
      <td>3.885781e-16</td>
      <td>-3.314016e-14</td>
    </tr>
    <tr>
      <th>iFF708</th>
      <td>1.776357e-15</td>
      <td>0.000000e+00</td>
      <td>2.838618e-12</td>
      <td>-5.329071e-14</td>
      <td>1.421085e-14</td>
      <td>5.329071e-15</td>
      <td>-4.263256e-14</td>
    </tr>
    <tr>
      <th>iGB555_fixed</th>
      <td>-1.037392e-12</td>
      <td>5.440199e-10</td>
      <td>4.702940e-10</td>
      <td>1.705303e-13</td>
      <td>-2.060574e-12</td>
      <td>2.700062e-13</td>
      <td>1.577405e-12</td>
    </tr>
    <tr>
      <th>iHD666_fixed</th>
      <td>3.774758e-14</td>
      <td>9.730550e-13</td>
      <td>1.013567e-08</td>
      <td>4.718448e-15</td>
      <td>-7.366330e-14</td>
      <td>3.164136e-15</td>
      <td>-2.220446e-16</td>
    </tr>
    <tr>
      <th>iIB711</th>
      <td>-1.421085e-14</td>
      <td>0.000000e+00</td>
      <td>2.015099e-11</td>
      <td>4.263256e-14</td>
      <td>-2.842171e-14</td>
      <td>-2.842171e-14</td>
      <td>-1.421085e-14</td>
    </tr>
    <tr>
      <th>iIT341</th>
      <td>-1.129519e-11</td>
      <td>2.245907e-10</td>
      <td>6.851687e-08</td>
      <td>-4.440892e-15</td>
      <td>-1.403899e-11</td>
      <td>-2.111644e-13</td>
      <td>-6.530149e-10</td>
    </tr>
    <tr>
      <th>iJL432</th>
      <td>-1.554312e-14</td>
      <td>0.000000e+00</td>
      <td>4.104939e-12</td>
      <td>-1.193490e-14</td>
      <td>2.103873e-14</td>
      <td>2.708944e-14</td>
      <td>1.809664e-13</td>
    </tr>
    <tr>
      <th>iJN678</th>
      <td>-4.718448e-16</td>
      <td>2.856902e-11</td>
      <td>2.463432e-08</td>
      <td>-1.082467e-15</td>
      <td>-2.220446e-16</td>
      <td>-2.775558e-17</td>
      <td>1.214445e-13</td>
    </tr>
    <tr>
      <th>iJN746</th>
      <td>1.231681e-10</td>
      <td>1.059390e-09</td>
      <td>2.485335e-08</td>
      <td>1.167688e-10</td>
      <td>7.149392e-11</td>
      <td>-6.661338e-15</td>
      <td>1.743801e-10</td>
    </tr>
    <tr>
      <th>iJO1366</th>
      <td>4.973799e-14</td>
      <td>1.739909e-10</td>
      <td>1.544051e-07</td>
      <td>8.881784e-16</td>
      <td>5.107026e-14</td>
      <td>-2.664535e-15</td>
      <td>5.774270e-13</td>
    </tr>
    <tr>
      <th>iJP815</th>
      <td>1.783040e-11</td>
      <td>0.000000e+00</td>
      <td>3.016005e-09</td>
      <td>2.160384e-10</td>
      <td>2.299161e-12</td>
      <td>3.759559e-11</td>
      <td>1.973555e-11</td>
    </tr>
    <tr>
      <th>iJR904</th>
      <td>-3.364420e-12</td>
      <td>2.154040e-10</td>
      <td>1.404389e-07</td>
      <td>1.258993e-13</td>
      <td>-3.852363e-11</td>
      <td>2.146194e-11</td>
      <td>3.302114e-11</td>
    </tr>
    <tr>
      <th>iJS747</th>
      <td>-1.421085e-13</td>
      <td>-9.758267e-09</td>
      <td>1.937650e-11</td>
      <td>-5.186962e-13</td>
      <td>7.105427e-15</td>
      <td>0.000000e+00</td>
      <td>-2.842171e-14</td>
    </tr>
    <tr>
      <th>iKF1028</th>
      <td>-1.799028e-11</td>
      <td>0.000000e+00</td>
      <td>4.904080e-09</td>
      <td>5.995204e-15</td>
      <td>-6.050105e-11</td>
      <td>6.877166e-11</td>
      <td>-3.783374e-11</td>
    </tr>
    <tr>
      <th>iLC915</th>
      <td>2.103206e-12</td>
      <td>0.000000e+00</td>
      <td>1.007605e-08</td>
      <td>-3.609557e-12</td>
      <td>3.211653e-12</td>
      <td>1.278977e-13</td>
      <td>2.231104e-11</td>
    </tr>
    <tr>
      <th>iLL672</th>
      <td>5.151435e-14</td>
      <td>-3.967990e-10</td>
      <td>2.029425e-09</td>
      <td>3.019807e-14</td>
      <td>4.529710e-14</td>
      <td>4.440892e-16</td>
      <td>-8.260059e-14</td>
    </tr>
    <tr>
      <th>iMA871</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>2.038192e-11</td>
      <td>-3.552714e-15</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>-1.065814e-14</td>
    </tr>
    <tr>
      <th>iMA945</th>
      <td>1.421085e-14</td>
      <td>0.000000e+00</td>
      <td>4.755066e-09</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>1.421085e-14</td>
      <td>9.947598e-14</td>
    </tr>
    <tr>
      <th>iMB745</th>
      <td>2.247508e-14</td>
      <td>0.000000e+00</td>
      <td>5.139368e-10</td>
      <td>4.757412e-10</td>
      <td>-2.697495e-14</td>
      <td>-2.733924e-15</td>
      <td>-3.323893e-12</td>
    </tr>
    <tr>
      <th>iMH551</th>
      <td>-4.263256e-14</td>
      <td>0.000000e+00</td>
      <td>2.145972e-11</td>
      <td>6.772360e-15</td>
      <td>-2.420286e-14</td>
      <td>4.440892e-16</td>
      <td>-2.721157e-13</td>
    </tr>
    <tr>
      <th>iMM1415</th>
      <td>-2.347234e-12</td>
      <td>0.000000e+00</td>
      <td>1.605315e-08</td>
      <td>5.881740e-12</td>
      <td>-1.929346e-11</td>
      <td>-6.439294e-15</td>
      <td>1.410982e-11</td>
    </tr>
    <tr>
      <th>iMM904</th>
      <td>1.060230e-11</td>
      <td>0.000000e+00</td>
      <td>2.990649e-09</td>
      <td>-9.992007e-15</td>
      <td>-9.139328e-11</td>
      <td>1.054712e-15</td>
      <td>-5.305936e-10</td>
    </tr>
    <tr>
      <th>iMO1056</th>
      <td>-7.860379e-14</td>
      <td>-6.367740e-10</td>
      <td>1.085125e-08</td>
      <td>-1.287859e-14</td>
      <td>5.107026e-15</td>
      <td>-2.664535e-15</td>
      <td>-3.352874e-14</td>
    </tr>
    <tr>
      <th>iMP429_fixed</th>
      <td>2.293721e-13</td>
      <td>0.000000e+00</td>
      <td>1.916863e-10</td>
      <td>-2.886580e-15</td>
      <td>1.887379e-15</td>
      <td>-1.443290e-15</td>
      <td>-3.357314e-13</td>
    </tr>
    <tr>
      <th>iND750</th>
      <td>-2.235294e-10</td>
      <td>3.722161e-13</td>
      <td>4.941149e-08</td>
      <td>-1.627079e-10</td>
      <td>3.478570e-11</td>
      <td>2.220446e-16</td>
      <td>-2.592769e-10</td>
    </tr>
    <tr>
      <th>iNJ661</th>
      <td>-5.478381e-11</td>
      <td>-1.366268e-14</td>
      <td>6.874230e-10</td>
      <td>1.412759e-14</td>
      <td>-1.110825e-11</td>
      <td>-2.481532e-10</td>
      <td>-3.497474e-10</td>
    </tr>
    <tr>
      <th>iNJ661m</th>
      <td>7.542578e-15</td>
      <td>-1.365574e-14</td>
      <td>1.140270e-08</td>
      <td>7.253811e-08</td>
      <td>1.649386e-07</td>
      <td>1.528997e-07</td>
      <td>-2.329942e-13</td>
    </tr>
    <tr>
      <th>iNV213</th>
      <td>8.881784e-15</td>
      <td>-8.495142e-10</td>
      <td>1.006306e-11</td>
      <td>0.000000e+00</td>
      <td>-8.881784e-15</td>
      <td>3.552714e-15</td>
      <td>-2.486900e-14</td>
    </tr>
    <tr>
      <th>iOG654</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
    </tr>
    <tr>
      <th>iOR363</th>
      <td>2.842171e-14</td>
      <td>0.000000e+00</td>
      <td>6.735945e-12</td>
      <td>-5.684342e-14</td>
      <td>-5.684342e-14</td>
      <td>-2.842171e-14</td>
      <td>2.842171e-14</td>
    </tr>
    <tr>
      <th>iPP668</th>
      <td>-3.552714e-15</td>
      <td>0.000000e+00</td>
      <td>1.800928e-10</td>
      <td>4.440892e-16</td>
      <td>3.597123e-14</td>
      <td>-7.549517e-15</td>
      <td>-7.238654e-14</td>
    </tr>
    <tr>
      <th>iPS189_fixed</th>
      <td>2.353673e-14</td>
      <td>-1.108655e-10</td>
      <td>9.894308e-12</td>
      <td>7.549517e-15</td>
      <td>9.015011e-14</td>
      <td>3.108624e-15</td>
      <td>1.656453e-13</td>
    </tr>
    <tr>
      <th>iRC1080</th>
      <td>-1.341149e-13</td>
      <td>9.275872e-09</td>
      <td>7.015366e-11</td>
      <td>5.062617e-13</td>
      <td>4.121148e-13</td>
      <td>6.838974e-14</td>
      <td>-1.287859e-13</td>
    </tr>
    <tr>
      <th>iRM588</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
    </tr>
    <tr>
      <th>iRR1083</th>
      <td>0.000000e+00</td>
      <td>1.977781e-08</td>
      <td>1.978151e-10</td>
      <td>0.000000e+00</td>
      <td>-2.842171e-14</td>
      <td>0.000000e+00</td>
      <td>-2.842171e-14</td>
    </tr>
    <tr>
      <th>iRS1563</th>
      <td>6.800116e-16</td>
      <td>0.000000e+00</td>
      <td>9.173981e-12</td>
      <td>-4.163336e-16</td>
      <td>5.967449e-16</td>
      <td>-9.478529e-15</td>
      <td>-8.118506e-15</td>
    </tr>
    <tr>
      <th>iRS1597</th>
      <td>3.552714e-15</td>
      <td>0.000000e+00</td>
      <td>9.791457e-11</td>
      <td>-8.881784e-15</td>
      <td>5.329071e-15</td>
      <td>-2.842171e-14</td>
      <td>-2.842171e-14</td>
    </tr>
    <tr>
      <th>iRS605_fixed</th>
      <td>1.199041e-14</td>
      <td>0.000000e+00</td>
      <td>4.111211e-09</td>
      <td>-2.975398e-14</td>
      <td>-3.996803e-15</td>
      <td>3.552714e-15</td>
      <td>-1.865175e-14</td>
    </tr>
    <tr>
      <th>iRsp1095</th>
      <td>-1.065814e-14</td>
      <td>1.172156e-09</td>
      <td>2.692957e-11</td>
      <td>-5.151435e-14</td>
      <td>1.421085e-14</td>
      <td>-2.131628e-14</td>
      <td>-8.526513e-14</td>
    </tr>
    <tr>
      <th>iSB619</th>
      <td>-3.088640e-13</td>
      <td>0.000000e+00</td>
      <td>9.349807e-11</td>
      <td>4.496403e-15</td>
      <td>-1.181277e-13</td>
      <td>1.437739e-14</td>
      <td>9.064693e-13</td>
    </tr>
    <tr>
      <th>iSH335</th>
      <td>3.552714e-15</td>
      <td>0.000000e+00</td>
      <td>9.279755e-11</td>
      <td>4.662937e-15</td>
      <td>-1.620926e-14</td>
      <td>-2.664535e-15</td>
      <td>4.016787e-13</td>
    </tr>
    <tr>
      <th>iSO783</th>
      <td>0.000000e+00</td>
      <td>-3.318235e-12</td>
      <td>7.798739e-10</td>
      <td>-5.684342e-14</td>
      <td>1.776357e-14</td>
      <td>0.000000e+00</td>
      <td>3.552714e-15</td>
    </tr>
    <tr>
      <th>iSR432</th>
      <td>-3.019807e-14</td>
      <td>-1.671046e-09</td>
      <td>4.089173e-12</td>
      <td>-2.167155e-13</td>
      <td>5.151435e-14</td>
      <td>-2.593481e-13</td>
      <td>-3.552714e-13</td>
    </tr>
    <tr>
      <th>iSS724</th>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>4.753531e-12</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
      <td>0.000000e+00</td>
    </tr>
    <tr>
      <th>iSS884</th>
      <td>1.421085e-13</td>
      <td>0.000000e+00</td>
      <td>6.156000e-10</td>
      <td>-1.563194e-13</td>
      <td>7.105427e-14</td>
      <td>-5.684342e-14</td>
      <td>-1.847411e-13</td>
    </tr>
    <tr>
      <th>iSyn669</th>
      <td>-6.186440e-13</td>
      <td>-1.463274e-12</td>
      <td>6.855544e-12</td>
      <td>-5.084516e-12</td>
      <td>6.528666e-13</td>
      <td>5.661027e-13</td>
      <td>-1.837835e-12</td>
    </tr>
    <tr>
      <th>iTH366</th>
      <td>3.274181e-11</td>
      <td>0.000000e+00</td>
      <td>2.655725e-10</td>
      <td>1.091394e-11</td>
      <td>1.455192e-11</td>
      <td>2.182787e-11</td>
      <td>1.818989e-11</td>
    </tr>
    <tr>
      <th>iTL885</th>
      <td>3.552714e-14</td>
      <td>6.856737e-13</td>
      <td>1.468498e-08</td>
      <td>8.881784e-14</td>
      <td>-4.973799e-14</td>
      <td>-1.572076e-13</td>
      <td>5.204726e-13</td>
    </tr>
    <tr>
      <th>iTY425_fixed</th>
      <td>-2.775558e-15</td>
      <td>0.000000e+00</td>
      <td>2.184031e-12</td>
      <td>2.775558e-15</td>
      <td>-5.551115e-16</td>
      <td>6.661338e-16</td>
      <td>2.079448e-13</td>
    </tr>
    <tr>
      <th>iVM679</th>
      <td>-2.398082e-14</td>
      <td>1.689826e-10</td>
      <td>1.038440e-10</td>
      <td>4.352074e-14</td>
      <td>7.549517e-15</td>
      <td>-2.131628e-14</td>
      <td>-3.819167e-14</td>
    </tr>
    <tr>
      <th>iVS941_fixed</th>
      <td>2.153833e-14</td>
      <td>0.000000e+00</td>
      <td>1.439289e-08</td>
      <td>3.785861e-14</td>
      <td>-3.352874e-14</td>
      <td>-1.498801e-14</td>
      <td>-3.141931e-14</td>
    </tr>
    <tr>
      <th>iWV1314</th>
      <td>5.329071e-14</td>
      <td>3.552714e-15</td>
      <td>4.255085e-11</td>
      <td>-3.552714e-15</td>
      <td>-3.552714e-15</td>
      <td>0.000000e+00</td>
      <td>-9.947598e-14</td>
    </tr>
    <tr>
      <th>iWZ663</th>
      <td>3.552714e-14</td>
      <td>2.741011e-09</td>
      <td>3.468870e-11</td>
      <td>8.526513e-14</td>
      <td>-5.684342e-14</td>
      <td>4.263256e-14</td>
      <td>-2.842171e-14</td>
    </tr>
    <tr>
      <th>iYL1228</th>
      <td>-7.904788e-14</td>
      <td>0.000000e+00</td>
      <td>2.068377e-09</td>
      <td>-1.332268e-15</td>
      <td>-1.265654e-14</td>
      <td>6.217249e-15</td>
      <td>-2.731149e-13</td>
    </tr>
    <tr>
      <th>iYO844</th>
      <td>-6.439294e-15</td>
      <td>-3.056155e-11</td>
      <td>4.923346e-10</td>
      <td>-1.554312e-15</td>
      <td>1.110223e-15</td>
      <td>6.661338e-16</td>
      <td>-3.130829e-14</td>
    </tr>
    <tr>
      <th>iZM363</th>
      <td>2.664535e-15</td>
      <td>0.000000e+00</td>
      <td>6.776801e-12</td>
      <td>-8.348877e-14</td>
      <td>7.549517e-15</td>
      <td>-2.220446e-15</td>
      <td>8.881784e-15</td>
    </tr>
    <tr>
      <th>iZmobMBEL601</th>
      <td>-1.004752e-14</td>
      <td>0.000000e+00</td>
      <td>2.098571e-11</td>
      <td>-3.115286e-13</td>
      <td>-3.136380e-14</td>
      <td>-4.996004e-15</td>
      <td>3.836931e-13</td>
    </tr>
    <tr>
      <th>mus_musculus</th>
      <td>-2.842171e-14</td>
      <td>0.000000e+00</td>
      <td>1.811600e-10</td>
      <td>-2.842171e-14</td>
      <td>0.000000e+00</td>
      <td>-2.842171e-14</td>
      <td>0.000000e+00</td>
    </tr>
    <tr>
      <th>textbook</th>
      <td>1.110223e-16</td>
      <td>9.818923e-12</td>
      <td>4.750644e-13</td>
      <td>0.000000e+00</td>
      <td>-1.110223e-16</td>
      <td>-1.110223e-16</td>
      <td>4.566791e-12</td>
    </tr>
  </tbody>
</table>
</div>




```python
abs(differences).max().max()
```




    3.6052116270113288e-07



0d5db150fcbb12bad9baa7a39e6b8b557b1924c0
ipynb
Jupyter Notebook
models/mmodel/exact_solving_models.ipynb
beatrizgj/memote-meta-study
fe16b3f2d1131e6b23333e49f3b5a3d1a93e33f1
Apache-2.0
2015-05-18T16:05:17.000Z
2020-11-23T08:52:09.000Z
models/mmodel/exact_solving_models.ipynb
beatrizgj/memote-meta-study
fe16b3f2d1131e6b23333e49f3b5a3d1a93e33f1
Apache-2.0
2015-07-09T13:56:12.000Z
2020-12-22T13:36:48.000Z
models/mmodel/exact_solving_models.ipynb
beatrizgj/memote-meta-study
fe16b3f2d1131e6b23333e49f3b5a3d1a93e33f1
Apache-2.0
2015-03-04T00:17:24.000Z
2021-08-02T18:00:08.000Z
Qwen/Qwen-72B
1. YES
2. YES