Average Error: 0.0 → 0.0
Time: 1.5s
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 r33979 = re;
        double r33980 = exp(r33979);
        double r33981 = im;
        double r33982 = cos(r33981);
        double r33983 = r33980 * r33982;
        return r33983;
}
↓
double f(double re, double im) {
        double r33984 = re;
        double r33985 = exp(r33984);
        double r33986 = im;
        double r33987 = cos(r33986);
        double r33988 = r33985 * r33987;
        return r33988;
}

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 2020018 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))