Average Error: 0.0 → 0.0
Time: 11.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)
double f(double re, double im) {
        double r1412792 = 0.5;
        double r1412793 = re;
        double r1412794 = cos(r1412793);
        double r1412795 = r1412792 * r1412794;
        double r1412796 = im;
        double r1412797 = -r1412796;
        double r1412798 = exp(r1412797);
        double r1412799 = exp(r1412796);
        double r1412800 = r1412798 + r1412799;
        double r1412801 = r1412795 * r1412800;
        return r1412801;
}
↓
double f(double re, double im) {
        double r1412802 = re;
        double r1412803 = cos(r1412802);
        double r1412804 = im;
        double r1412805 = exp(r1412804);
        double r1412806 = 0.5;
        double r1412807 = r1412805 * r1412806;
        double r1412808 = r1412806 / r1412805;
        double r1412809 = r1412807 + r1412808;
        double r1412810 = r1412803 * r1412809;
        return r1412810;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))