Average Error: 0.0 → 0.0
Time: 12.7s
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 r1281770 = 0.5;
        double r1281771 = re;
        double r1281772 = cos(r1281771);
        double r1281773 = r1281770 * r1281772;
        double r1281774 = im;
        double r1281775 = -r1281774;
        double r1281776 = exp(r1281775);
        double r1281777 = exp(r1281774);
        double r1281778 = r1281776 + r1281777;
        double r1281779 = r1281773 * r1281778;
        return r1281779;
}
↓
double f(double re, double im) {
        double r1281780 = re;
        double r1281781 = cos(r1281780);
        double r1281782 = 0.5;
        double r1281783 = im;
        double r1281784 = exp(r1281783);
        double r1281785 = r1281782 / r1281784;
        double r1281786 = r1281782 * r1281784;
        double r1281787 = r1281785 + r1281786;
        double r1281788 = r1281781 * r1281787;
        return r1281788;
}

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 2019135 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))