Average Error: 0.0 → 0.0
Time: 18.9s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\left(e^{im} + e^{-im}\right) \cdot \left(0.5 \cdot \cos re\right)
double f(double re, double im) {
        double r1154622 = 0.5;
        double r1154623 = re;
        double r1154624 = cos(r1154623);
        double r1154625 = r1154622 * r1154624;
        double r1154626 = im;
        double r1154627 = -r1154626;
        double r1154628 = exp(r1154627);
        double r1154629 = exp(r1154626);
        double r1154630 = r1154628 + r1154629;
        double r1154631 = r1154625 * r1154630;
        return r1154631;
}
↓
double f(double re, double im) {
        double r1154632 = im;
        double r1154633 = exp(r1154632);
        double r1154634 = -r1154632;
        double r1154635 = exp(r1154634);
        double r1154636 = r1154633 + r1154635;
        double r1154637 = 0.5;
        double r1154638 = re;
        double r1154639 = cos(r1154638);
        double r1154640 = r1154637 * r1154639;
        double r1154641 = r1154636 * r1154640;
        return r1154641;
}

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

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

Reproduce

herbie shell --seed 2019142 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))