Average Error: 0.0 → 0.0
Time: 13.7s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\left(\left|\sqrt[3]{e^{re}}\right| \cdot \sqrt{\sqrt[3]{e^{re}}}\right) \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]
e^{re} \cdot \cos im
↓
\left(\left|\sqrt[3]{e^{re}}\right| \cdot \sqrt{\sqrt[3]{e^{re}}}\right) \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)
double f(double re, double im) {
        double r3206427 = re;
        double r3206428 = exp(r3206427);
        double r3206429 = im;
        double r3206430 = cos(r3206429);
        double r3206431 = r3206428 * r3206430;
        return r3206431;
}
↓
double f(double re, double im) {
        double r3206432 = re;
        double r3206433 = exp(r3206432);
        double r3206434 = cbrt(r3206433);
        double r3206435 = fabs(r3206434);
        double r3206436 = sqrt(r3206434);
        double r3206437 = r3206435 * r3206436;
        double r3206438 = sqrt(r3206433);
        double r3206439 = im;
        double r3206440 = cos(r3206439);
        double r3206441 = r3206438 * r3206440;
        double r3206442 = r3206437 * r3206441;
        return r3206442;
}

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. Using strategy rm

  6. Applied add-cube-cbrt0.0

    \[\leadsto \sqrt{\color{blue}{\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \sqrt[3]{e^{re}}}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]

  7. Applied sqrt-prod0.0

    \[\leadsto \color{blue}{\left(\sqrt{\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}} \cdot \sqrt{\sqrt[3]{e^{re}}}\right)} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]

  8. Simplified0.0

    \[\leadsto \left(\color{blue}{\left|\sqrt[3]{e^{re}}\right|} \cdot \sqrt{\sqrt[3]{e^{re}}}\right) \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]

  9. Final simplification0.0

    \[\leadsto \left(\left|\sqrt[3]{e^{re}}\right| \cdot \sqrt{\sqrt[3]{e^{re}}}\right) \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]

Reproduce

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