Average Error: 0.0 → 0.0
Time: 38.1s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot e^{im} + \left(0.5 \cdot \cos re\right) \cdot e^{-im}\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in0.0

    \[\leadsto \color{blue}{e^{-im} \cdot \left(0.5 \cdot \cos re\right) + e^{im} \cdot \left(0.5 \cdot \cos re\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot e^{im} + \left(0.5 \cdot \cos re\right) \cdot e^{-im}\]

Reproduce

herbie shell --seed 2019091 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))