Average Error: 0.0 → 0.0

Time: 18.2s

Precision: 64

Internal Precision: 128

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

↓

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

Error

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

Derivation

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

Reproduce

herbie shell --seed 2019091 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))