Average Error: 0.0 → 0.0

Time: 9.2s

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 r446527 = re;
        double r446528 = exp(r446527);
        double r446529 = im;
        double r446530 = cos(r446529);
        double r446531 = r446528 * r446530;
        return r446531;
}

↓

double f(double re, double im) {
        double r446532 = im;
        double r446533 = cos(r446532);
        double r446534 = re;
        double r446535 = exp(r446534);
        double r446536 = r446533 * r446535;
        return r446536;
}

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 2019112 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))