Average Error: 0.0 → 0.0
Time: 9.3s
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 r1034430 = re;
        double r1034431 = exp(r1034430);
        double r1034432 = im;
        double r1034433 = cos(r1034432);
        double r1034434 = r1034431 * r1034433;
        return r1034434;
}
↓
double f(double re, double im) {
        double r1034435 = im;
        double r1034436 = cos(r1034435);
        double r1034437 = re;
        double r1034438 = exp(r1034437);
        double r1034439 = r1034436 * r1034438;
        return r1034439;
}

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 2019134 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))