Average Error: 0.0 → 0.0
Time: 8.6s
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 r1049728 = re;
        double r1049729 = exp(r1049728);
        double r1049730 = im;
        double r1049731 = cos(r1049730);
        double r1049732 = r1049729 * r1049731;
        return r1049732;
}
↓
double f(double re, double im) {
        double r1049733 = im;
        double r1049734 = cos(r1049733);
        double r1049735 = re;
        double r1049736 = exp(r1049735);
        double r1049737 = r1049734 * r1049736;
        return r1049737;
}

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 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))