Average Error: 0.0 → 0.1
Time: 1.5m
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \sqrt[3]{{\left(e^{im} + e^{-im}\right)}^{3}}\]

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. Using strategy rm

  3. Applied add-cbrt-cube0.1

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

  4. Applied simplify0.1

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

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed '#(1072840222 1305617769 1692503039 1353360431 4178980589 1488672652)' 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))