Average Error: 0.0 → 0.0
Time: 12.3s
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 r41910 = re;
        double r41911 = exp(r41910);
        double r41912 = im;
        double r41913 = cos(r41912);
        double r41914 = r41911 * r41913;
        return r41914;
}
↓
double f(double re, double im) {
        double r41915 = re;
        double r41916 = exp(r41915);
        double r41917 = im;
        double r41918 = cos(r41917);
        double r41919 = r41916 * r41918;
        return r41919;
}

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 2019306 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))