Average Error: 0.0 → 0.1
Time: 14.4s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
\left(\sqrt[3]{e^{re}} \cdot \sqrt[3]{e^{re}}\right) \cdot \left(\sqrt[3]{e^{re}} \cdot \sin im\right)
double f(double re, double im) {
        double r1532872 = re;
        double r1532873 = exp(r1532872);
        double r1532874 = im;
        double r1532875 = sin(r1532874);
        double r1532876 = r1532873 * r1532875;
        return r1532876;
}
↓
double f(double re, double im) {
        double r1532877 = re;
        double r1532878 = exp(r1532877);
        double r1532879 = cbrt(r1532878);
        double r1532880 = r1532879 * r1532879;
        double r1532881 = im;
        double r1532882 = sin(r1532881);
        double r1532883 = r1532879 * r1532882;
        double r1532884 = r1532880 * r1532883;
        return r1532884;
}

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-cbrt0.1

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

  4. Applied associate-*l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))