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 r739224 = re;
        double r739225 = exp(r739224);
        double r739226 = im;
        double r739227 = cos(r739226);
        double r739228 = r739225 * r739227;
        return r739228;
}

↓

double f(double re, double im) {
        double r739229 = im;
        double r739230 = cos(r739229);
        double r739231 = re;
        double r739232 = exp(r739231);
        double r739233 = r739230 * r739232;
        return r739233;
}

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 2019121 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))