Average Error: 0.0 → 0.0
Time: 40.4s
Precision: 64
Internal Precision: 128
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(\sqrt[3]{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}} \cdot \sqrt[3]{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}}\right) \cdot \left(\cos re \cdot \sqrt[3]{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}}\right)\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{0.5}{e^{im}} + e^{im} \cdot 0.5\right) \cdot \cos re}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.0

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5} \cdot \sqrt[3]{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5}\right) \cdot \sqrt[3]{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5}\right)} \cdot \cos re\]

  5. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5} \cdot \sqrt[3]{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5}\right) \cdot \left(\sqrt[3]{\frac{0.5}{e^{im}} + e^{im} \cdot 0.5} \cdot \cos re\right)}\]

  6. Final simplification0.0

    \[\leadsto \left(\sqrt[3]{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}} \cdot \sqrt[3]{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}}\right) \cdot \left(\cos re \cdot \sqrt[3]{\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}}\right)\]

Reproduce

herbie shell --seed 2019068 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))