Average Error: 0.0 → 0.0
Time: 9.7s
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 r70592 = 0.5;
        double r70593 = re;
        double r70594 = cos(r70593);
        double r70595 = r70592 * r70594;
        double r70596 = im;
        double r70597 = -r70596;
        double r70598 = exp(r70597);
        double r70599 = exp(r70596);
        double r70600 = r70598 + r70599;
        double r70601 = r70595 * r70600;
        return r70601;
}
↓
double f(double re, double im) {
        double r70602 = 0.5;
        double r70603 = re;
        double r70604 = cos(r70603);
        double r70605 = r70602 * r70604;
        double r70606 = im;
        double r70607 = -r70606;
        double r70608 = exp(r70607);
        double r70609 = exp(r70606);
        double r70610 = r70608 + r70609;
        double r70611 = r70605 * r70610;
        return r70611;
}

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 2020045 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))