Average Error: 0.0 → 0.0

Time: 6.9s

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 r799826 = re;
        double r799827 = exp(r799826);
        double r799828 = im;
        double r799829 = cos(r799828);
        double r799830 = r799827 * r799829;
        return r799830;
}

↓

double f(double re, double im) {
        double r799831 = im;
        double r799832 = cos(r799831);
        double r799833 = re;
        double r799834 = exp(r799833);
        double r799835 = r799832 * r799834;
        return r799835;
}

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 2019153 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))