Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\sin re \cdot \left(0.5 \cdot \left(e^{im} + e^{-im}\right)\right)\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied *-commutative0.0

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

  4. Applied associate-*l*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019088 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))