Average Error: 0.0 → 0.0

Time: 15.6s

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 r743670 = re;
        double r743671 = exp(r743670);
        double r743672 = im;
        double r743673 = cos(r743672);
        double r743674 = r743671 * r743673;
        return r743674;
}

↓

double f(double re, double im) {
        double r743675 = im;
        double r743676 = cos(r743675);
        double r743677 = re;
        double r743678 = exp(r743677);
        double r743679 = r743676 * r743678;
        return r743679;
}

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 2019151 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))