Average Error: 0.0 → 0.0
Time: 22.5s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(\frac{\cos re}{e^{im}} + e^{im} \cdot \cos re\right) \cdot 0.5\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(\frac{\cos re}{e^{im}} + e^{im} \cdot \cos re\right) \cdot 0.5
double f(double re, double im) {
        double r2813906 = 0.5;
        double r2813907 = re;
        double r2813908 = cos(r2813907);
        double r2813909 = r2813906 * r2813908;
        double r2813910 = im;
        double r2813911 = -r2813910;
        double r2813912 = exp(r2813911);
        double r2813913 = exp(r2813910);
        double r2813914 = r2813912 + r2813913;
        double r2813915 = r2813909 * r2813914;
        return r2813915;
}
↓
double f(double re, double im) {
        double r2813916 = re;
        double r2813917 = cos(r2813916);
        double r2813918 = im;
        double r2813919 = exp(r2813918);
        double r2813920 = r2813917 / r2813919;
        double r2813921 = r2813919 * r2813917;
        double r2813922 = r2813920 + r2813921;
        double r2813923 = 0.5;
        double r2813924 = r2813922 * r2813923;
        return r2813924;
}

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. Using strategy rm

  3. Applied associate-*l*0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019132 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))