Average Error: 0.0 → 0.0

Time: 4.5s

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 r486942 = re;
        double r486943 = exp(r486942);
        double r486944 = im;
        double r486945 = cos(r486944);
        double r486946 = r486943 * r486945;
        return r486946;
}

↓

double f(double re, double im) {
        double r486947 = im;
        double r486948 = cos(r486947);
        double r486949 = re;
        double r486950 = exp(r486949);
        double r486951 = r486948 * r486950;
        return r486951;
}

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 2019119 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))