Average Error: 0.0 → 0.0
Time: 16.2s
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 r2097675 = re;
        double r2097676 = exp(r2097675);
        double r2097677 = im;
        double r2097678 = cos(r2097677);
        double r2097679 = r2097676 * r2097678;
        return r2097679;
}
↓
double f(double re, double im) {
        double r2097680 = im;
        double r2097681 = cos(r2097680);
        double r2097682 = re;
        double r2097683 = exp(r2097682);
        double r2097684 = r2097681 * r2097683;
        return r2097684;
}

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 2019170 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))