Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[e^{re} \cdot \sin im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sin im \cdot \sqrt{e^{re}}\right)\]
e^{re} \cdot \sin im
↓
\sqrt{e^{re}} \cdot \left(\sin im \cdot \sqrt{e^{re}}\right)
double f(double re, double im) {
        double r1815839 = re;
        double r1815840 = exp(r1815839);
        double r1815841 = im;
        double r1815842 = sin(r1815841);
        double r1815843 = r1815840 * r1815842;
        return r1815843;
}
↓
double f(double re, double im) {
        double r1815844 = re;
        double r1815845 = exp(r1815844);
        double r1815846 = sqrt(r1815845);
        double r1815847 = im;
        double r1815848 = sin(r1815847);
        double r1815849 = r1815848 * r1815846;
        double r1815850 = r1815846 * r1815849;
        return r1815850;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))