Average Error: 0.0 → 0.0
Time: 9.0s
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 r1915616 = re;
        double r1915617 = exp(r1915616);
        double r1915618 = im;
        double r1915619 = cos(r1915618);
        double r1915620 = r1915617 * r1915619;
        return r1915620;
}
↓
double f(double re, double im) {
        double r1915621 = im;
        double r1915622 = cos(r1915621);
        double r1915623 = re;
        double r1915624 = exp(r1915623);
        double r1915625 = r1915622 * r1915624;
        return r1915625;
}

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 2019142 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))