Average Error: 0.0 → 0.0

Time: 1.0m

Precision: 64

Internal Precision: 576

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

↓

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

Error

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

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Derivation

Initial program 0.0
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
Initial simplification0.0
\[\leadsto (\left(0.5 \cdot \sin re\right) \cdot \left(e^{im}\right) + \left(\frac{\sin re}{\frac{e^{im}}{0.5}}\right))_*\]
Using strategy rm
Applied fma-udef0.0
\[\leadsto \color{blue}{\left(0.5 \cdot \sin re\right) \cdot e^{im} + \frac{\sin re}{\frac{e^{im}}{0.5}}}\]
Final simplification0.0
\[\leadsto \frac{\sin re}{\frac{e^{im}}{0.5}} + \left(0.5 \cdot \sin re\right) \cdot e^{im}\]

Runtime

herbie shell --seed 2018234 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))