Average Error: 0.0 → 0.0
Time: 15.6s
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 r1807818 = 0.5;
        double r1807819 = re;
        double r1807820 = cos(r1807819);
        double r1807821 = r1807818 * r1807820;
        double r1807822 = im;
        double r1807823 = -r1807822;
        double r1807824 = exp(r1807823);
        double r1807825 = exp(r1807822);
        double r1807826 = r1807824 + r1807825;
        double r1807827 = r1807821 * r1807826;
        return r1807827;
}
↓
double f(double re, double im) {
        double r1807828 = re;
        double r1807829 = cos(r1807828);
        double r1807830 = 0.5;
        double r1807831 = im;
        double r1807832 = exp(r1807831);
        double r1807833 = r1807830 / r1807832;
        double r1807834 = r1807830 * r1807832;
        double r1807835 = r1807833 + r1807834;
        double r1807836 = r1807829 * r1807835;
        return r1807836;
}

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 2019172 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))