Average Error: 0.0 → 0.0
Time: 19.0s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]
e^{re} \cdot \cos im
↓
\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)
double f(double re, double im) {
        double r35372 = re;
        double r35373 = exp(r35372);
        double r35374 = im;
        double r35375 = cos(r35374);
        double r35376 = r35373 * r35375;
        return r35376;
}
↓
double f(double re, double im) {
        double r35377 = re;
        double r35378 = exp(r35377);
        double r35379 = sqrt(r35378);
        double r35380 = im;
        double r35381 = cos(r35380);
        double r35382 = r35379 * r35381;
        double r35383 = r35379 * r35382;
        return r35383;
}

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

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))