Average Error: 0.0 → 0.0
Time: 14.3s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{0.5 \cdot \cos re}{e^{im}}\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
e^{im} \cdot \left(0.5 \cdot \cos re\right) + \frac{0.5 \cdot \cos re}{e^{im}}
double f(double re, double im) {
        double r5200778 = 0.5;
        double r5200779 = re;
        double r5200780 = cos(r5200779);
        double r5200781 = r5200778 * r5200780;
        double r5200782 = im;
        double r5200783 = -r5200782;
        double r5200784 = exp(r5200783);
        double r5200785 = exp(r5200782);
        double r5200786 = r5200784 + r5200785;
        double r5200787 = r5200781 * r5200786;
        return r5200787;
}
↓
double f(double re, double im) {
        double r5200788 = im;
        double r5200789 = exp(r5200788);
        double r5200790 = 0.5;
        double r5200791 = re;
        double r5200792 = cos(r5200791);
        double r5200793 = r5200790 * r5200792;
        double r5200794 = r5200789 * r5200793;
        double r5200795 = r5200793 / r5200789;
        double r5200796 = r5200794 + r5200795;
        return r5200796;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))