Average Error: 0.0 → 0.0

Time: 11.4s

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 r37133 = re;
        double r37134 = exp(r37133);
        double r37135 = im;
        double r37136 = cos(r37135);
        double r37137 = r37134 * r37136;
        return r37137;
}

↓

double f(double re, double im) {
        double r37138 = im;
        double r37139 = cos(r37138);
        double r37140 = re;
        double r37141 = exp(r37140);
        double r37142 = r37139 * r37141;
        return r37142;
}

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 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))