Average Error: 0.0 → 0.0
Time: 10.9s
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 r50450 = 0.5;
        double r50451 = re;
        double r50452 = cos(r50451);
        double r50453 = r50450 * r50452;
        double r50454 = im;
        double r50455 = -r50454;
        double r50456 = exp(r50455);
        double r50457 = exp(r50454);
        double r50458 = r50456 + r50457;
        double r50459 = r50453 * r50458;
        return r50459;
}
↓
double f(double re, double im) {
        double r50460 = 0.5;
        double r50461 = re;
        double r50462 = cos(r50461);
        double r50463 = r50460 * r50462;
        double r50464 = im;
        double r50465 = -r50464;
        double r50466 = exp(r50465);
        double r50467 = exp(r50464);
        double r50468 = r50466 + r50467;
        double r50469 = r50463 * r50468;
        return r50469;
}

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 2019294 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))