Average Error: 0.0 → 0.0

Time: 6.1s

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 r436938 = re;
        double r436939 = exp(r436938);
        double r436940 = im;
        double r436941 = cos(r436940);
        double r436942 = r436939 * r436941;
        return r436942;
}

↓

double f(double re, double im) {
        double r436943 = im;
        double r436944 = cos(r436943);
        double r436945 = re;
        double r436946 = exp(r436945);
        double r436947 = r436944 * r436946;
        return r436947;
}

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 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))