Average Error: 0.0 → 0.0

Time: 10.4s

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 r479313 = re;
        double r479314 = exp(r479313);
        double r479315 = im;
        double r479316 = cos(r479315);
        double r479317 = r479314 * r479316;
        return r479317;
}

↓

double f(double re, double im) {
        double r479318 = im;
        double r479319 = cos(r479318);
        double r479320 = re;
        double r479321 = exp(r479320);
        double r479322 = r479319 * r479321;
        return r479322;
}

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 2019120 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))