Average Error: 0.0 → 0.0
Time: 8.5s
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 r1315032 = re;
        double r1315033 = exp(r1315032);
        double r1315034 = im;
        double r1315035 = cos(r1315034);
        double r1315036 = r1315033 * r1315035;
        return r1315036;
}
↓
double f(double re, double im) {
        double r1315037 = im;
        double r1315038 = cos(r1315037);
        double r1315039 = re;
        double r1315040 = exp(r1315039);
        double r1315041 = r1315038 * r1315040;
        return r1315041;
}

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 2019129 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))