Average Error: 0.0 → 0.1
Time: 3.6s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt[3]{{\left(e^{re}\right)}^{2}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
\sqrt[3]{{\left(e^{re}\right)}^{2}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)
double f(double re, double im) {
        double r60823 = re;
        double r60824 = exp(r60823);
        double r60825 = im;
        double r60826 = sin(r60825);
        double r60827 = r60824 * r60826;
        return r60827;
}
↓
double f(double re, double im) {
        double r60828 = re;
        double r60829 = exp(r60828);
        double r60830 = 2.0;
        double r60831 = pow(r60829, r60830);
        double r60832 = cbrt(r60831);
        double r60833 = cbrt(r60829);
        double r60834 = im;
        double r60835 = sin(r60834);
        double r60836 = r60833 * r60835;
        double r60837 = r60832 * r60836;
        return r60837;
}

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

    \[e^{re} \cdot \sin im\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

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

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)}\]
  5. Using strategy rm

  6. Applied cbrt-unprod0.1

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

  7. Simplified0.1

    \[\leadsto \sqrt[3]{\color{blue}{{\left(e^{re}\right)}^{2}}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]

  8. Final simplification0.1

    \[\leadsto \sqrt[3]{{\left(e^{re}\right)}^{2}} \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]

Reproduce

herbie shell --seed 2020036 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))