Average Error: 0.0 → 0.0
Time: 4.6s
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 r1774773 = re;
        double r1774774 = exp(r1774773);
        double r1774775 = im;
        double r1774776 = sin(r1774775);
        double r1774777 = r1774774 * r1774776;
        return r1774777;
}
↓
double f(double re, double im) {
        double r1774778 = re;
        double r1774779 = exp(r1774778);
        double r1774780 = sqrt(r1774779);
        double r1774781 = im;
        double r1774782 = sin(r1774781);
        double r1774783 = r1774782 * r1774780;
        double r1774784 = r1774780 * r1774783;
        return r1774784;
}

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 2019171 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  (* (exp re) (sin im)))