Average Error: 0.0 → 0.0
Time: 12.4s
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 r1745464 = re;
        double r1745465 = exp(r1745464);
        double r1745466 = im;
        double r1745467 = cos(r1745466);
        double r1745468 = r1745465 * r1745467;
        return r1745468;
}
↓
double f(double re, double im) {
        double r1745469 = im;
        double r1745470 = cos(r1745469);
        double r1745471 = re;
        double r1745472 = exp(r1745471);
        double r1745473 = r1745470 * r1745472;
        return r1745473;
}

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 2019138 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))