Average Error: 0.0 → 0.1
Time: 11.3s
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 r1490187 = re;
        double r1490188 = exp(r1490187);
        double r1490189 = im;
        double r1490190 = sin(r1490189);
        double r1490191 = r1490188 * r1490190;
        return r1490191;
}
↓
double f(double re, double im) {
        double r1490192 = re;
        double r1490193 = exp(r1490192);
        double r1490194 = cbrt(r1490193);
        double r1490195 = r1490194 * r1490194;
        double r1490196 = im;
        double r1490197 = sin(r1490196);
        double r1490198 = r1490194 * r1490197;
        double r1490199 = r1490195 * r1490198;
        return r1490199;
}

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)))