Average Error: 0.0 → 0.0

Time: 3.4s

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 r702033 = re;
        double r702034 = exp(r702033);
        double r702035 = im;
        double r702036 = cos(r702035);
        double r702037 = r702034 * r702036;
        return r702037;
}

↓

double f(double re, double im) {
        double r702038 = im;
        double r702039 = cos(r702038);
        double r702040 = re;
        double r702041 = exp(r702040);
        double r702042 = r702039 * r702041;
        return r702042;
}

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 2019154 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))