Average Error: 0.0 → 0.0
Time: 28.2s
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 r3437912 = 0.5;
        double r3437913 = re;
        double r3437914 = cos(r3437913);
        double r3437915 = r3437912 * r3437914;
        double r3437916 = im;
        double r3437917 = -r3437916;
        double r3437918 = exp(r3437917);
        double r3437919 = exp(r3437916);
        double r3437920 = r3437918 + r3437919;
        double r3437921 = r3437915 * r3437920;
        return r3437921;
}
↓
double f(double re, double im) {
        double r3437922 = re;
        double r3437923 = cos(r3437922);
        double r3437924 = 0.5;
        double r3437925 = im;
        double r3437926 = exp(r3437925);
        double r3437927 = r3437924 / r3437926;
        double r3437928 = r3437924 * r3437926;
        double r3437929 = r3437927 + r3437928;
        double r3437930 = r3437923 * r3437929;
        return r3437930;
}

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 2019128 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))