Average Error: 0.0 → 0.0
Time: 1.2s
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 r78431 = re;
        double r78432 = exp(r78431);
        double r78433 = im;
        double r78434 = cos(r78433);
        double r78435 = r78432 * r78434;
        return r78435;
}
↓
double f(double re, double im) {
        double r78436 = re;
        double r78437 = exp(r78436);
        double r78438 = im;
        double r78439 = cos(r78438);
        double r78440 = r78437 * r78439;
        return r78440;
}

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 2020021 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))