Average Error: 0.0 → 0.0
Time: 20.2s
Precision: 64
Internal Precision: 384
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\frac{\sin re}{\frac{e^{im}}{0.5}} + e^{im} \cdot \left(0.5 \cdot \sin re\right)\]

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. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Applied simplify0.0

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

Runtime

Time bar (total: 20.2s)Debug logProfile

herbie shell --seed '#(1070706311 3771791028 4128836681 4194990999 2341756049 504035650)' 
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))