Average Error: 0.0 → 0.0
Time: 33.6s
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 r2404891 = 0.5;
        double r2404892 = re;
        double r2404893 = cos(r2404892);
        double r2404894 = r2404891 * r2404893;
        double r2404895 = im;
        double r2404896 = -r2404895;
        double r2404897 = exp(r2404896);
        double r2404898 = exp(r2404895);
        double r2404899 = r2404897 + r2404898;
        double r2404900 = r2404894 * r2404899;
        return r2404900;
}
↓
double f(double re, double im) {
        double r2404901 = re;
        double r2404902 = cos(r2404901);
        double r2404903 = 0.5;
        double r2404904 = im;
        double r2404905 = exp(r2404904);
        double r2404906 = r2404903 / r2404905;
        double r2404907 = r2404903 * r2404905;
        double r2404908 = r2404906 + r2404907;
        double r2404909 = r2404902 * r2404908;
        return r2404909;
}

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))))