Average Error: 0.0 → 0.0

Time: 24.7s

Precision: 64

Internal Precision: 128

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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `re`

Derivation

Initial program 0.0
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
Taylor expanded around -inf 0.0
\[\leadsto \color{blue}{0.5 \cdot \left(\sin re \cdot \left(e^{im} + e^{-1 \cdot im}\right)\right)}\]
Simplified0.0
\[\leadsto \color{blue}{(\left(e^{im}\right) \cdot 0.5 + \left(\frac{0.5}{e^{im}}\right))_* \cdot \sin re}\]
Final simplification0.0
\[\leadsto \sin re \cdot (\left(e^{im}\right) \cdot 0.5 + \left(\frac{0.5}{e^{im}}\right))_*\]

Reproduce

herbie shell --seed 2019090 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))