Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[e^{re} \cdot \cos im\]
e^{re} \cdot \cos im
↓
e^{re} \cdot \cos im
double f(double re, double im) {
        double r78224 = re;
        double r78225 = exp(r78224);
        double r78226 = im;
        double r78227 = cos(r78226);
        double r78228 = r78225 * r78227;
        return r78228;
}
↓
double f(double re, double im) {
        double r78229 = re;
        double r78230 = exp(r78229);
        double r78231 = im;
        double r78232 = cos(r78231);
        double r78233 = r78230 * r78232;
        return r78233;
}

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

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))