Average Error: 0.0 → 0.0
Time: 3.0s
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 r1285465 = re;
        double r1285466 = exp(r1285465);
        double r1285467 = im;
        double r1285468 = cos(r1285467);
        double r1285469 = r1285466 * r1285468;
        return r1285469;
}
↓
double f(double re, double im) {
        double r1285470 = im;
        double r1285471 = cos(r1285470);
        double r1285472 = re;
        double r1285473 = exp(r1285472);
        double r1285474 = r1285471 * r1285473;
        return r1285474;
}

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 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))