Average Error: 0.0 → 0.0
Time: 9.7s
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 r1635591 = re;
        double r1635592 = exp(r1635591);
        double r1635593 = im;
        double r1635594 = cos(r1635593);
        double r1635595 = r1635592 * r1635594;
        return r1635595;
}
↓
double f(double re, double im) {
        double r1635596 = im;
        double r1635597 = cos(r1635596);
        double r1635598 = re;
        double r1635599 = exp(r1635598);
        double r1635600 = r1635597 * r1635599;
        return r1635600;
}

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)))