Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)
double f(double re, double im) {
        double r44676 = 0.5;
        double r44677 = re;
        double r44678 = cos(r44677);
        double r44679 = r44676 * r44678;
        double r44680 = im;
        double r44681 = -r44680;
        double r44682 = exp(r44681);
        double r44683 = exp(r44680);
        double r44684 = r44682 + r44683;
        double r44685 = r44679 * r44684;
        return r44685;
}
↓
double f(double re, double im) {
        double r44686 = 0.5;
        double r44687 = re;
        double r44688 = cos(r44687);
        double r44689 = r44686 * r44688;
        double r44690 = -1.0;
        double r44691 = im;
        double r44692 = r44690 * r44691;
        double r44693 = exp(r44692);
        double r44694 = exp(r44691);
        double r44695 = r44693 + r44694;
        double r44696 = r44689 * r44695;
        return r44696;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around inf 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))