Average Error: 0.0 → 0.0
Time: 11.9s
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 r42293 = re;
        double r42294 = exp(r42293);
        double r42295 = im;
        double r42296 = sin(r42295);
        double r42297 = r42294 * r42296;
        return r42297;
}
↓
double f(double re, double im) {
        double r42298 = re;
        double r42299 = exp(r42298);
        double r42300 = sqrt(r42299);
        double r42301 = im;
        double r42302 = sin(r42301);
        double r42303 = r42300 * r42302;
        double r42304 = r42300 * r42303;
        return r42304;
}

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 2019235 
(FPCore (re im)
  :name "math.exp on complex, imaginary part"
  :precision binary64
  (* (exp re) (sin im)))