Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)\]
e^{re} \cdot \cos im
↓
\sqrt{e^{re}} \cdot \left(\sqrt{e^{re}} \cdot \cos im\right)
double f(double re, double im) {
        double r54891 = re;
        double r54892 = exp(r54891);
        double r54893 = im;
        double r54894 = cos(r54893);
        double r54895 = r54892 * r54894;
        return r54895;
}
↓
double f(double re, double im) {
        double r54896 = re;
        double r54897 = exp(r54896);
        double r54898 = sqrt(r54897);
        double r54899 = im;
        double r54900 = cos(r54899);
        double r54901 = r54898 * r54900;
        double r54902 = r54898 * r54901;
        return r54902;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(FPCore (re im)
  :name "math.exp on complex, real part"
  :precision binary64
  (* (exp re) (cos im)))