Average Error: 0.0 → 0.0
Time: 20.7s
Precision: 64
\[e^{re} \cdot \cos im\]
↓
\[e^{\log \left(\sqrt{e^{re}}\right)} \cdot \left(e^{\log \left(\sqrt{e^{re}}\right)} \cdot \cos im\right)\]
e^{re} \cdot \cos im
↓
e^{\log \left(\sqrt{e^{re}}\right)} \cdot \left(e^{\log \left(\sqrt{e^{re}}\right)} \cdot \cos im\right)
double f(double re, double im) {
        double r38822 = re;
        double r38823 = exp(r38822);
        double r38824 = im;
        double r38825 = cos(r38824);
        double r38826 = r38823 * r38825;
        return r38826;
}
↓
double f(double re, double im) {
        double r38827 = re;
        double r38828 = exp(r38827);
        double r38829 = sqrt(r38828);
        double r38830 = log(r38829);
        double r38831 = exp(r38830);
        double r38832 = im;
        double r38833 = cos(r38832);
        double r38834 = r38831 * r38833;
        double r38835 = r38831 * r38834;
        return r38835;
}

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

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

  8. Applied add-exp-log0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (re im)
  :name "math.exp on complex, real part"
  (* (exp re) (cos im)))