Average Error: 0.0 → 0.0

Time: 9.0s

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 r778258 = re;
        double r778259 = exp(r778258);
        double r778260 = im;
        double r778261 = cos(r778260);
        double r778262 = r778259 * r778261;
        return r778262;
}

↓

double f(double re, double im) {
        double r778263 = im;
        double r778264 = cos(r778263);
        double r778265 = re;
        double r778266 = exp(r778265);
        double r778267 = r778264 * r778266;
        return r778267;
}

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 2019132 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))