Error

Derivation

1. Initial program 0.0

   \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

2. Initial simplification0.0

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

4. Applied add-sqr-sqrt0.0

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

5. Applied associate-/r*0.0

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

6. Final simplification0.0

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

Runtime

Time bar (total: 25.1s)Debug logProfile

herbie shell --seed 2018254 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))