Average Error: 0.0 → 0.0
Time: 9.8s
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 r1875826 = re;
        double r1875827 = exp(r1875826);
        double r1875828 = im;
        double r1875829 = cos(r1875828);
        double r1875830 = r1875827 * r1875829;
        return r1875830;
}
↓
double f(double re, double im) {
        double r1875831 = im;
        double r1875832 = cos(r1875831);
        double r1875833 = re;
        double r1875834 = exp(r1875833);
        double r1875835 = r1875832 * r1875834;
        return r1875835;
}

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 2019158 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))