Catalyzes the conversion of 1-hydroxy-2-methyl-2-(E)-butenyl 4-diphosphate (HMBPP) into a mixture of isopentenyl diphosphate (IPP) and dimethylallyl diphosphate (DMAPP). Acts in the terminal step of the DOXP/MEP pathway for isoprenoid precursor biosynthesis. H2O + isopentenyl diphosphate + 2 oxidized [2Fe-2S]-[ferredoxin] = (2E)-4-hydroxy-3-methylbut-2-enyl diphosphate + 2 H(+) + 2 reduced [2Fe-2S]-[ferredoxin] dimethylallyl diphosphate + H2O + 2 oxidized [2Fe-2S]-[ferredoxin] = (2E)-4-hydroxy-3-methylbut-2-enyl diphosphate + 2 H(+) + 2 reduced [2Fe-2S]-[ferredoxin] Binds 1 [4Fe-4S] cluster per subunit. Isoprenoid biosynthesis; dimethylallyl diphosphate biosynthesis; dimethylallyl diphosphate from (2E)-4-hydroxy-3-methylbutenyl diphosphate: step 1/1. Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via DXP pathway; isopentenyl diphosphate from 1-deoxy-D-xylulose 5-phosphate: step 6/6. Belongs to the IspH family. Extended N-terminus.