Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)\]
e^{re} \cdot \sin im
↓
\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \sin im\right)
double f(double re, double im) {
        double r47980 = re;
        double r47981 = exp(r47980);
        double r47982 = im;
        double r47983 = sin(r47982);
        double r47984 = r47981 * r47983;
        return r47984;
}
↓
double f(double re, double im) {
        double r47985 = re;
        double r47986 = exp(r47985);
        double r47987 = sqrt(r47986);
        double r47988 = im;
        double r47989 = sin(r47988);
        double r47990 = r47987 * r47989;
        double r47991 = r47987 * r47990;
        return r47991;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))