Average Error: 0.0 → 0.0
Time: 9.8s
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 r1842461 = re;
        double r1842462 = exp(r1842461);
        double r1842463 = im;
        double r1842464 = cos(r1842463);
        double r1842465 = r1842462 * r1842464;
        return r1842465;
}
↓
double f(double re, double im) {
        double r1842466 = im;
        double r1842467 = cos(r1842466);
        double r1842468 = re;
        double r1842469 = exp(r1842468);
        double r1842470 = r1842467 * r1842469;
        return r1842470;
}

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 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))