Average Error: 0.0 → 0.0
Time: 22.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} \cdot \cos re + \frac{\cos re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r1118813 = 0.5;
        double r1118814 = re;
        double r1118815 = cos(r1118814);
        double r1118816 = r1118813 * r1118815;
        double r1118817 = im;
        double r1118818 = -r1118817;
        double r1118819 = exp(r1118818);
        double r1118820 = exp(r1118817);
        double r1118821 = r1118819 + r1118820;
        double r1118822 = r1118816 * r1118821;
        return r1118822;
}
↓
double f(double re, double im) {
        double r1118823 = im;
        double r1118824 = exp(r1118823);
        double r1118825 = re;
        double r1118826 = cos(r1118825);
        double r1118827 = r1118824 * r1118826;
        double r1118828 = r1118826 / r1118824;
        double r1118829 = r1118827 + r1118828;
        double r1118830 = 0.5;
        double r1118831 = r1118829 * r1118830;
        return r1118831;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))