Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
double f(double re, double im) {
        double r81703 = 0.5;
        double r81704 = re;
        double r81705 = cos(r81704);
        double r81706 = r81703 * r81705;
        double r81707 = im;
        double r81708 = -r81707;
        double r81709 = exp(r81708);
        double r81710 = exp(r81707);
        double r81711 = r81709 + r81710;
        double r81712 = r81706 * r81711;
        return r81712;
}
↓
double f(double re, double im) {
        double r81713 = 0.5;
        double r81714 = re;
        double r81715 = cos(r81714);
        double r81716 = r81713 * r81715;
        double r81717 = im;
        double r81718 = -r81717;
        double r81719 = exp(r81718);
        double r81720 = exp(r81717);
        double r81721 = r81719 + r81720;
        double r81722 = r81716 * r81721;
        return r81722;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020059 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))