Average Error: 0.0 → 0.0
Time: 13.8s
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 r1702851 = re;
        double r1702852 = exp(r1702851);
        double r1702853 = im;
        double r1702854 = sin(r1702853);
        double r1702855 = r1702852 * r1702854;
        return r1702855;
}
↓
double f(double re, double im) {
        double r1702856 = re;
        double r1702857 = exp(r1702856);
        double r1702858 = sqrt(r1702857);
        double r1702859 = im;
        double r1702860 = sin(r1702859);
        double r1702861 = r1702860 * r1702858;
        double r1702862 = r1702858 * r1702861;
        return r1702862;
}

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)))