Average Error: 0.0 → 0.0
Time: 18.2s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[(\left(0.5 \cdot \sin re\right) \cdot \left(e^{im}\right) + \left(\frac{0.5 \cdot \sin re}{e^{im}}\right))_*\]

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. Initial simplification0.0

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

  3. Final simplification0.0

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

Runtime

Time bar (total: 18.2s)Debug logProfile

herbie shell --seed 2018217 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))