Average Error: 0.0 → 0.1
Time: 30.4s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[(\left(e^{im}\right) \cdot \left(\sin re\right) + \left(\sin re \cdot \sqrt[3]{\left(\frac{1}{e^{im}} \cdot \frac{1}{e^{im}}\right) \cdot \frac{1}{e^{im}}}\right))_* \cdot 0.5\]

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

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

  4. Applied div-inv0.0

    \[\leadsto 0.5 \cdot (\left(e^{im}\right) \cdot \left(\sin re\right) + \color{blue}{\left(\sin re \cdot \frac{1}{e^{im}}\right)})_*\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.1

    \[\leadsto 0.5 \cdot (\left(e^{im}\right) \cdot \left(\sin re\right) + \left(\sin re \cdot \color{blue}{\sqrt[3]{\left(\frac{1}{e^{im}} \cdot \frac{1}{e^{im}}\right) \cdot \frac{1}{e^{im}}}}\right))_*\]

  7. Final simplification0.1

    \[\leadsto (\left(e^{im}\right) \cdot \left(\sin re\right) + \left(\sin re \cdot \sqrt[3]{\left(\frac{1}{e^{im}} \cdot \frac{1}{e^{im}}\right) \cdot \frac{1}{e^{im}}}\right))_* \cdot 0.5\]

Runtime

Time bar (total: 30.4s)Debug logProfile

herbie shell --seed 2018346 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))