Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\left(\cos im \cdot e^{\log \left(\sqrt{e^{re}}\right)}\right) \cdot \sqrt{e^{re}}\]
e^{re} \cdot \cos im
↓
\left(\cos im \cdot e^{\log \left(\sqrt{e^{re}}\right)}\right) \cdot \sqrt{e^{re}}
double f(double re, double im) {
        double r2322873 = re;
        double r2322874 = exp(r2322873);
        double r2322875 = im;
        double r2322876 = cos(r2322875);
        double r2322877 = r2322874 * r2322876;
        return r2322877;
}
↓
double f(double re, double im) {
        double r2322878 = im;
        double r2322879 = cos(r2322878);
        double r2322880 = re;
        double r2322881 = exp(r2322880);
        double r2322882 = sqrt(r2322881);
        double r2322883 = log(r2322882);
        double r2322884 = exp(r2322883);
        double r2322885 = r2322879 * r2322884;
        double r2322886 = r2322885 * r2322882;
        return r2322886;
}

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

    \[e^{re} \cdot \cos im\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*l*0.0

    \[\leadsto \color{blue}{\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)}\]
  5. Using strategy rm

  6. Applied add-exp-log0.0

    \[\leadsto \sqrt{e^{re}} \cdot \left(\color{blue}{e^{\log \left(\sqrt{e^{re}}\right)}} \cdot \cos im\right)\]

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))