Average Error: 0.0 → 0.0
Time: 12.9s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\left(\cos im \cdot \left|\sqrt[3]{e^{re}}\right|\right) \cdot \sqrt{\sqrt[3]{e^{re}}}\right)\]
e^{re} \cdot \cos im
↓
\sqrt{e^{re}} \cdot \left(\left(\cos im \cdot \left|\sqrt[3]{e^{re}}\right|\right) \cdot \sqrt{\sqrt[3]{e^{re}}}\right)
double f(double re, double im) {
        double r47277 = re;
        double r47278 = exp(r47277);
        double r47279 = im;
        double r47280 = cos(r47279);
        double r47281 = r47278 * r47280;
        return r47281;
}
↓
double f(double re, double im) {
        double r47282 = re;
        double r47283 = exp(r47282);
        double r47284 = sqrt(r47283);
        double r47285 = im;
        double r47286 = cos(r47285);
        double r47287 = cbrt(r47283);
        double r47288 = fabs(r47287);
        double r47289 = r47286 * r47288;
        double r47290 = sqrt(r47287);
        double r47291 = r47289 * r47290;
        double r47292 = r47284 * r47291;
        return r47292;
}

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. Simplified0.0

    \[\leadsto \sqrt{e^{re}} \cdot \color{blue}{\left(\cos im \cdot \sqrt{e^{re}}\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.0

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

  8. Applied sqrt-prod0.0

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

  9. Applied associate-*r*0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

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