Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[e^{re} \cdot \cos im\]
\[\cos im \cdot e^{re}\]
double f(double re, double im) {
        double r377970 = re;
        double r377971 = exp(r377970);
        double r377972 = im;
        double r377973 = cos(r377972);
        double r377974 = r377971 * r377973;
        return r377974;
}

double f(double re, double im) {
        double r377975 = im;
        double r377976 = cos(r377975);
        double r377977 = re;
        double r377978 = exp(r377977);
        double r377979 = r377976 * r377978;
        return r377979;
}

e^{re} \cdot \cos im
\cos im \cdot e^{re}

Error

Bits error versus re

Bits error versus im

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 2019101 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))