Average Error: 0.0 → 0.0
Time: 2.7s
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 r1103440 = re;
        double r1103441 = exp(r1103440);
        double r1103442 = im;
        double r1103443 = cos(r1103442);
        double r1103444 = r1103441 * r1103443;
        return r1103444;
}
↓
double f(double re, double im) {
        double r1103445 = im;
        double r1103446 = cos(r1103445);
        double r1103447 = re;
        double r1103448 = exp(r1103447);
        double r1103449 = r1103446 * r1103448;
        return r1103449;
}

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 2019162 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))