Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]
\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)
↓
\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)
double f(double re, double im) {
        double r2087354 = 0.5;
        double r2087355 = re;
        double r2087356 = cos(r2087355);
        double r2087357 = r2087354 * r2087356;
        double r2087358 = im;
        double r2087359 = -r2087358;
        double r2087360 = exp(r2087359);
        double r2087361 = exp(r2087358);
        double r2087362 = r2087360 + r2087361;
        double r2087363 = r2087357 * r2087362;
        return r2087363;
}
↓
double f(double re, double im) {
        double r2087364 = re;
        double r2087365 = cos(r2087364);
        double r2087366 = im;
        double r2087367 = exp(r2087366);
        double r2087368 = 0.5;
        double r2087369 = r2087367 * r2087368;
        double r2087370 = r2087368 / r2087367;
        double r2087371 = r2087369 + r2087370;
        double r2087372 = r2087365 * r2087371;
        return r2087372;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)}\]

  3. Final simplification0.0

    \[\leadsto \cos re \cdot \left(e^{im} \cdot 0.5 + \frac{0.5}{e^{im}}\right)\]

Reproduce

herbie shell --seed 2019192 
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))