Average Error: 0.0 → 0.0

Time: 8.5s

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 r724127 = re;
        double r724128 = exp(r724127);
        double r724129 = im;
        double r724130 = cos(r724129);
        double r724131 = r724128 * r724130;
        return r724131;
}

↓

double f(double re, double im) {
        double r724132 = im;
        double r724133 = cos(r724132);
        double r724134 = re;
        double r724135 = exp(r724134);
        double r724136 = r724133 * r724135;
        return r724136;
}

Error

The X axis uses an exponential scale — Bits error versus `re`

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 0.0
\[e^{re} \cdot \cos im\]
Final simplification0.0
\[\leadsto \cos im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))