Average Error: 0.0 → 0.0

Time: 2.8s

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 r909855 = re;
        double r909856 = exp(r909855);
        double r909857 = im;
        double r909858 = cos(r909857);
        double r909859 = r909856 * r909858;
        return r909859;
}

↓

double f(double re, double im) {
        double r909860 = im;
        double r909861 = cos(r909860);
        double r909862 = re;
        double r909863 = exp(r909862);
        double r909864 = r909861 * r909863;
        return r909864;
}

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 2019171 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))