Average Error: 0.0 → 0.0

Time: 3.3s

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 r559472 = re;
        double r559473 = exp(r559472);
        double r559474 = im;
        double r559475 = cos(r559474);
        double r559476 = r559473 * r559475;
        return r559476;
}

↓

double f(double re, double im) {
        double r559477 = im;
        double r559478 = cos(r559477);
        double r559479 = re;
        double r559480 = exp(r559479);
        double r559481 = r559478 * r559480;
        return r559481;
}

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 2019156 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))