Average Error: 0.0 → 0.0
Time: 21.0s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\cos im \cdot \sqrt{e^{re}}\right)\]
e^{re} \cdot \cos im
↓
\sqrt{e^{re}} \cdot \left(\cos im \cdot \sqrt{e^{re}}\right)
double f(double re, double im) {
        double r3297398 = re;
        double r3297399 = exp(r3297398);
        double r3297400 = im;
        double r3297401 = cos(r3297400);
        double r3297402 = r3297399 * r3297401;
        return r3297402;
}
↓
double f(double re, double im) {
        double r3297403 = re;
        double r3297404 = exp(r3297403);
        double r3297405 = sqrt(r3297404);
        double r3297406 = im;
        double r3297407 = cos(r3297406);
        double r3297408 = r3297407 * r3297405;
        double r3297409 = r3297405 * r3297408;
        return r3297409;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{re}} \cdot \sqrt{e^{re}}\right)} \cdot \cos im\]

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)}\]

  5. Final simplification0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\cos im \cdot \sqrt{e^{re}}\right)\]

Reproduce

herbie shell --seed 2019174 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))