Average Error: 0.0 → 0.0
Time: 12.2s
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 r1141315 = re;
        double r1141316 = exp(r1141315);
        double r1141317 = im;
        double r1141318 = cos(r1141317);
        double r1141319 = r1141316 * r1141318;
        return r1141319;
}
↓
double f(double re, double im) {
        double r1141320 = im;
        double r1141321 = cos(r1141320);
        double r1141322 = re;
        double r1141323 = exp(r1141322);
        double r1141324 = r1141321 * r1141323;
        return r1141324;
}

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 2019124 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))