Average Error: 0.0 → 0.0
Time: 22.2s
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 r2347377 = 0.5;
        double r2347378 = re;
        double r2347379 = cos(r2347378);
        double r2347380 = r2347377 * r2347379;
        double r2347381 = im;
        double r2347382 = -r2347381;
        double r2347383 = exp(r2347382);
        double r2347384 = exp(r2347381);
        double r2347385 = r2347383 + r2347384;
        double r2347386 = r2347380 * r2347385;
        return r2347386;
}
↓
double f(double re, double im) {
        double r2347387 = im;
        double r2347388 = exp(r2347387);
        double r2347389 = -r2347387;
        double r2347390 = exp(r2347389);
        double r2347391 = r2347388 + r2347390;
        double r2347392 = 0.5;
        double r2347393 = re;
        double r2347394 = cos(r2347393);
        double r2347395 = r2347392 * r2347394;
        double r2347396 = r2347391 * r2347395;
        return r2347396;
}

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 2019158 +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))