Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[e^{re} \cdot \sin im\]
e^{re} \cdot \sin im
↓
e^{re} \cdot \sin im
double f(double re, double im) {
        double r44892 = re;
        double r44893 = exp(r44892);
        double r44894 = im;
        double r44895 = sin(r44894);
        double r44896 = r44893 * r44895;
        return r44896;
}
↓
double f(double re, double im) {
        double r44897 = re;
        double r44898 = exp(r44897);
        double r44899 = im;
        double r44900 = sin(r44899);
        double r44901 = r44898 * r44900;
        return r44901;
}

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-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

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

  6. Applied associate-*r*0.0

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

  7. Simplified0.0

    \[\leadsto \color{blue}{e^{re}} \cdot \sin im\]

  8. Final simplification0.0

    \[\leadsto e^{re} \cdot \sin im\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))