Average Error: 0.0 → 0.0
Time: 4.6s
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 r1614868 = re;
        double r1614869 = exp(r1614868);
        double r1614870 = im;
        double r1614871 = cos(r1614870);
        double r1614872 = r1614869 * r1614871;
        return r1614872;
}
↓
double f(double re, double im) {
        double r1614873 = im;
        double r1614874 = cos(r1614873);
        double r1614875 = re;
        double r1614876 = exp(r1614875);
        double r1614877 = r1614874 * r1614876;
        return r1614877;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{re} \cdot \cos im\]

  2. Final simplification0.0

    \[\leadsto \cos im \cdot e^{re}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))