Average Error: 0.0 → 0.0
Time: 8.9s
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 r1428306 = re;
        double r1428307 = exp(r1428306);
        double r1428308 = im;
        double r1428309 = cos(r1428308);
        double r1428310 = r1428307 * r1428309;
        return r1428310;
}
↓
double f(double re, double im) {
        double r1428311 = im;
        double r1428312 = cos(r1428311);
        double r1428313 = re;
        double r1428314 = exp(r1428313);
        double r1428315 = r1428312 * r1428314;
        return r1428315;
}

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 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))