Average Error: 0.0 → 0.0
Time: 1.7m
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re}{\frac{e^{im}}{0.5}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

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 distribute-lft-in0.0

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

  4. Applied simplify0.0

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

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))