Average Error: 0.1 → 0.1
Time: 5.7s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \sin re\right)\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.1

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

  2. Applied simplify0.1

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

Runtime

Time bar (total: 5.7s)Debug logProfile

herbie shell --seed '#(1071725047 233389029 2036512464 3988615230 2972226563 1111574017)' +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))