Average Error: 0.0 → 0.0

Time: 2.6s

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 r976293 = re;
        double r976294 = exp(r976293);
        double r976295 = im;
        double r976296 = cos(r976295);
        double r976297 = r976294 * r976296;
        return r976297;
}

↓

double f(double re, double im) {
        double r976298 = im;
        double r976299 = cos(r976298);
        double r976300 = re;
        double r976301 = exp(r976300);
        double r976302 = r976299 * r976301;
        return r976302;
}

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 2019171 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))