Average Error: 0.0 → 0.0
Time: 17.1s
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 r1092882 = re;
        double r1092883 = exp(r1092882);
        double r1092884 = im;
        double r1092885 = cos(r1092884);
        double r1092886 = r1092883 * r1092885;
        return r1092886;
}
↓
double f(double re, double im) {
        double r1092887 = im;
        double r1092888 = cos(r1092887);
        double r1092889 = re;
        double r1092890 = exp(r1092889);
        double r1092891 = r1092888 * r1092890;
        return r1092891;
}

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 2019144 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))