Average Error: 0.0 → 0.0
Time: 14.5s
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 r1616128 = re;
        double r1616129 = exp(r1616128);
        double r1616130 = im;
        double r1616131 = cos(r1616130);
        double r1616132 = r1616129 * r1616131;
        return r1616132;
}
↓
double f(double re, double im) {
        double r1616133 = im;
        double r1616134 = cos(r1616133);
        double r1616135 = re;
        double r1616136 = exp(r1616135);
        double r1616137 = r1616134 * r1616136;
        return r1616137;
}

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 2019135 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))