Average Error: 0.0 → 0.0
Time: 32.4s
Precision: 64
Internal Precision: 384
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re}{e^{im}} \cdot 0.5 + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

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

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

Runtime

Time bar (total: 32.4s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))