Average Error: 0.0 → 0.0
Time: 18.6s
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 r717370 = 0.5;
        double r717371 = re;
        double r717372 = cos(r717371);
        double r717373 = r717370 * r717372;
        double r717374 = im;
        double r717375 = -r717374;
        double r717376 = exp(r717375);
        double r717377 = exp(r717374);
        double r717378 = r717376 + r717377;
        double r717379 = r717373 * r717378;
        return r717379;
}
↓
double f(double re, double im) {
        double r717380 = im;
        double r717381 = exp(r717380);
        double r717382 = -r717380;
        double r717383 = exp(r717382);
        double r717384 = r717381 + r717383;
        double r717385 = 0.5;
        double r717386 = re;
        double r717387 = cos(r717386);
        double r717388 = r717385 * r717387;
        double r717389 = r717384 * r717388;
        return r717389;
}

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