Average Error: 0.0 → 0.0
Time: 25.0s
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 r1647666 = 0.5;
        double r1647667 = re;
        double r1647668 = cos(r1647667);
        double r1647669 = r1647666 * r1647668;
        double r1647670 = im;
        double r1647671 = -r1647670;
        double r1647672 = exp(r1647671);
        double r1647673 = exp(r1647670);
        double r1647674 = r1647672 + r1647673;
        double r1647675 = r1647669 * r1647674;
        return r1647675;
}
↓
double f(double re, double im) {
        double r1647676 = re;
        double r1647677 = cos(r1647676);
        double r1647678 = 0.5;
        double r1647679 = im;
        double r1647680 = exp(r1647679);
        double r1647681 = r1647678 / r1647680;
        double r1647682 = r1647678 * r1647680;
        double r1647683 = r1647681 + r1647682;
        double r1647684 = r1647677 * r1647683;
        return r1647684;
}

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