Average Error: 0.0 → 0.0
Time: 19.5s
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 r48344 = 0.5;
        double r48345 = re;
        double r48346 = cos(r48345);
        double r48347 = r48344 * r48346;
        double r48348 = im;
        double r48349 = -r48348;
        double r48350 = exp(r48349);
        double r48351 = exp(r48348);
        double r48352 = r48350 + r48351;
        double r48353 = r48347 * r48352;
        return r48353;
}
↓
double f(double re, double im) {
        double r48354 = 0.5;
        double r48355 = re;
        double r48356 = cos(r48355);
        double r48357 = r48354 * r48356;
        double r48358 = im;
        double r48359 = -r48358;
        double r48360 = exp(r48359);
        double r48361 = exp(r48358);
        double r48362 = r48360 + r48361;
        double r48363 = r48357 * r48362;
        return r48363;
}

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 2019325 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))