Average Error: 0.0 → 0.0

Time: 14.4s

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 r811564 = re;
        double r811565 = exp(r811564);
        double r811566 = im;
        double r811567 = cos(r811566);
        double r811568 = r811565 * r811567;
        return r811568;
}

↓

double f(double re, double im) {
        double r811569 = im;
        double r811570 = cos(r811569);
        double r811571 = re;
        double r811572 = exp(r811571);
        double r811573 = r811570 * r811572;
        return r811573;
}

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 2019130 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))