Error

Derivation

1. Initial program 0.0

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

2. Initial simplification0.0

   \[\leadsto (\left(e^{im}\right) \cdot \left(\cos re \cdot 0.5\right) + \left(\frac{\cos re \cdot 0.5}{e^{im}}\right))_*\]
3. Using strategy rm

4. Applied *-un-lft-identity0.0

   \[\leadsto (\left(e^{im}\right) \cdot \left(\cos re \cdot 0.5\right) + \left(\frac{\cos re \cdot 0.5}{\color{blue}{1 \cdot e^{im}}}\right))_*\]

5. Applied times-frac0.0

   \[\leadsto (\left(e^{im}\right) \cdot \left(\cos re \cdot 0.5\right) + \color{blue}{\left(\frac{\cos re}{1} \cdot \frac{0.5}{e^{im}}\right)})_*\]

6. Simplified0.0

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

7. Final simplification0.0

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

Runtime

Time bar (total: 20.1s)Debug logProfile

herbie shell --seed 2018353 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))