Average Error: 0.0 → 0.0
Time: 10.7s
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 r48279 = 0.5;
        double r48280 = re;
        double r48281 = cos(r48280);
        double r48282 = r48279 * r48281;
        double r48283 = im;
        double r48284 = -r48283;
        double r48285 = exp(r48284);
        double r48286 = exp(r48283);
        double r48287 = r48285 + r48286;
        double r48288 = r48282 * r48287;
        return r48288;
}
↓
double f(double re, double im) {
        double r48289 = 0.5;
        double r48290 = re;
        double r48291 = cos(r48290);
        double r48292 = r48289 * r48291;
        double r48293 = im;
        double r48294 = -r48293;
        double r48295 = exp(r48294);
        double r48296 = exp(r48293);
        double r48297 = r48295 + r48296;
        double r48298 = r48292 * r48297;
        return r48298;
}

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 2020047 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))