Average Error: 0.0 → 0.0

Time: 6.8m

Precision: 64

Internal Precision: 128

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

↓

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

Error

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

Derivation

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

Reproduce

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