Average Error: 0.0 → 0.0

Time: 16.4s

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 r992167 = re;
        double r992168 = exp(r992167);
        double r992169 = im;
        double r992170 = cos(r992169);
        double r992171 = r992168 * r992170;
        return r992171;
}

↓

double f(double re, double im) {
        double r992172 = im;
        double r992173 = cos(r992172);
        double r992174 = re;
        double r992175 = exp(r992174);
        double r992176 = r992173 * r992175;
        return r992176;
}

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 2019149 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))