Average Error: 0.0 → 0.0
Time: 48.4s
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 r2505521 = 0.5;
        double r2505522 = re;
        double r2505523 = cos(r2505522);
        double r2505524 = r2505521 * r2505523;
        double r2505525 = im;
        double r2505526 = -r2505525;
        double r2505527 = exp(r2505526);
        double r2505528 = exp(r2505525);
        double r2505529 = r2505527 + r2505528;
        double r2505530 = r2505524 * r2505529;
        return r2505530;
}
↓
double f(double re, double im) {
        double r2505531 = re;
        double r2505532 = cos(r2505531);
        double r2505533 = 0.5;
        double r2505534 = im;
        double r2505535 = exp(r2505534);
        double r2505536 = r2505533 / r2505535;
        double r2505537 = r2505533 * r2505535;
        double r2505538 = r2505536 + r2505537;
        double r2505539 = r2505532 * r2505538;
        return r2505539;
}

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 2019124 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))