Average Error: 0.0 → 0.0
Time: 6.8s
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 r60683 = 0.5;
        double r60684 = re;
        double r60685 = cos(r60684);
        double r60686 = r60683 * r60685;
        double r60687 = im;
        double r60688 = -r60687;
        double r60689 = exp(r60688);
        double r60690 = exp(r60687);
        double r60691 = r60689 + r60690;
        double r60692 = r60686 * r60691;
        return r60692;
}
↓
double f(double re, double im) {
        double r60693 = 0.5;
        double r60694 = re;
        double r60695 = cos(r60694);
        double r60696 = r60693 * r60695;
        double r60697 = im;
        double r60698 = -r60697;
        double r60699 = exp(r60698);
        double r60700 = exp(r60697);
        double r60701 = r60699 + r60700;
        double r60702 = r60696 * r60701;
        return r60702;
}

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 2019318 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))