Average Error: 0.0 → 0.0
Time: 4.4s
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 r63403 = 0.5;
        double r63404 = re;
        double r63405 = cos(r63404);
        double r63406 = r63403 * r63405;
        double r63407 = im;
        double r63408 = -r63407;
        double r63409 = exp(r63408);
        double r63410 = exp(r63407);
        double r63411 = r63409 + r63410;
        double r63412 = r63406 * r63411;
        return r63412;
}
↓
double f(double re, double im) {
        double r63413 = 0.5;
        double r63414 = re;
        double r63415 = cos(r63414);
        double r63416 = r63413 * r63415;
        double r63417 = im;
        double r63418 = -r63417;
        double r63419 = exp(r63418);
        double r63420 = exp(r63417);
        double r63421 = r63419 + r63420;
        double r63422 = r63416 * r63421;
        return r63422;
}

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 2020065 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))