Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\cos im \cdot e^{re}\]
e^{re} \cdot \cos im
↓
\cos im \cdot e^{re}
double f(double re, double im) {
        double r1127517 = re;
        double r1127518 = exp(r1127517);
        double r1127519 = im;
        double r1127520 = cos(r1127519);
        double r1127521 = r1127518 * r1127520;
        return r1127521;
}
↓
double f(double re, double im) {
        double r1127522 = im;
        double r1127523 = cos(r1127522);
        double r1127524 = re;
        double r1127525 = exp(r1127524);
        double r1127526 = r1127523 * r1127525;
        return r1127526;
}

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

    \[e^{re} \cdot \cos im\]

  2. Final simplification0.0

    \[\leadsto \cos im \cdot e^{re}\]

Reproduce

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