Average Error: 0.0 → 0.0

Time: 8.7s

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 r790536 = re;
        double r790537 = exp(r790536);
        double r790538 = im;
        double r790539 = cos(r790538);
        double r790540 = r790537 * r790539;
        return r790540;
}

↓

double f(double re, double im) {
        double r790541 = im;
        double r790542 = cos(r790541);
        double r790543 = re;
        double r790544 = exp(r790543);
        double r790545 = r790542 * r790544;
        return r790545;
}

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 2019139 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))