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 r738070 = re;
        double r738071 = exp(r738070);
        double r738072 = im;
        double r738073 = cos(r738072);
        double r738074 = r738071 * r738073;
        return r738074;
}

↓

double f(double re, double im) {
        double r738075 = im;
        double r738076 = cos(r738075);
        double r738077 = re;
        double r738078 = exp(r738077);
        double r738079 = r738076 * r738078;
        return r738079;
}

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)))