Average Error: 0.0 → 0.1
Time: 1.1m
Precision: 64
Internal Precision: 320
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \sqrt[3]{{\left(\frac{(\left(e^{im}\right) \cdot \left(e^{im}\right) + 1)_*}{e^{im}}\right)}^{3}}\]

Error

Bits error versus re

Bits error versus im

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

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

    \[\leadsto \left(0.5 \cdot \cos re\right) \cdot \sqrt[3]{\color{blue}{{\left(\frac{(\left(e^{im}\right) \cdot \left(e^{im}\right) + 1)_*}{e^{im}}\right)}^{3}}}\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))