Average Error: 0.0 → 0.0
Time: 8.2s
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 r1574977 = re;
        double r1574978 = exp(r1574977);
        double r1574979 = im;
        double r1574980 = cos(r1574979);
        double r1574981 = r1574978 * r1574980;
        return r1574981;
}
↓
double f(double re, double im) {
        double r1574982 = im;
        double r1574983 = cos(r1574982);
        double r1574984 = re;
        double r1574985 = exp(r1574984);
        double r1574986 = r1574983 * r1574985;
        return r1574986;
}

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)))