Average Error: 0.0 → 0.0
Time: 34.6s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(\frac{0.5}{e^{im}} + 0.5 \cdot e^{im}\right)
double f(double re, double im) {
        double r2433723 = 0.5;
        double r2433724 = re;
        double r2433725 = cos(r2433724);
        double r2433726 = r2433723 * r2433725;
        double r2433727 = im;
        double r2433728 = -r2433727;
        double r2433729 = exp(r2433728);
        double r2433730 = exp(r2433727);
        double r2433731 = r2433729 + r2433730;
        double r2433732 = r2433726 * r2433731;
        return r2433732;
}
↓
double f(double re, double im) {
        double r2433733 = re;
        double r2433734 = cos(r2433733);
        double r2433735 = 0.5;
        double r2433736 = im;
        double r2433737 = exp(r2433736);
        double r2433738 = r2433735 / r2433737;
        double r2433739 = r2433735 * r2433737;
        double r2433740 = r2433738 + r2433739;
        double r2433741 = r2433734 * r2433740;
        return r2433741;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019107 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))