Average Error: 0.0 → 0.1
Time: 19.7s
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 r96088 = re;
        double r96089 = exp(r96088);
        double r96090 = im;
        double r96091 = sin(r96090);
        double r96092 = r96089 * r96091;
        return r96092;
}
↓
double f(double re, double im) {
        double r96093 = re;
        double r96094 = exp(r96093);
        double r96095 = cbrt(r96094);
        double r96096 = r96095 * r96095;
        double r96097 = im;
        double r96098 = sin(r96097);
        double r96099 = r96095 * r96098;
        double r96100 = r96096 * r96099;
        return r96100;
}

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 2019209 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))