Average Error: 0.0 → 0.0
Time: 1.5m
Precision: 64
Internal Precision: 320
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[0.5 \cdot \left(\left(e^{im} + e^{-im}\right) \cdot \sin re\right)\]

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 associate-*l*0.0

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

  4. Applied simplify0.0

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

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed '#(1071821486 549052472 3784827256 1559736200 3548510075 881134285)' 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))