Average Error: 0.0 → 0.1
Time: 1.9m
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \frac{{\left(e^{-im}\right)}^{3} + {\left(e^{im}\right)}^{3}}{\left(e^{im + im} + \left(-1\right)\right) - \frac{-1}{e^{im + im}}}\]

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 flip3-+0.1

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

  4. Applied simplify0.1

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed '#(1071821486 549052472 3784827256 1559736200 3548510075 881134285)' 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))