Average Error: 16.9 → 12.9
Time: 28.8s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \sqrt[3]{\frac{\sqrt{1}}{F}}\right) \cdot \left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \sqrt[3]{\frac{\sqrt{1}}{F}}\right) \cdot \left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)
double f(double F, double l) {
        double r32818 = atan2(1.0, 0.0);
        double r32819 = l;
        double r32820 = r32818 * r32819;
        double r32821 = 1.0;
        double r32822 = F;
        double r32823 = r32822 * r32822;
        double r32824 = r32821 / r32823;
        double r32825 = tan(r32820);
        double r32826 = r32824 * r32825;
        double r32827 = r32820 - r32826;
        return r32827;
}
↓
double f(double F, double l) {
        double r32828 = atan2(1.0, 0.0);
        double r32829 = l;
        double r32830 = r32828 * r32829;
        double r32831 = 1.0;
        double r32832 = sqrt(r32831);
        double r32833 = F;
        double r32834 = r32832 / r32833;
        double r32835 = cbrt(r32834);
        double r32836 = r32835 * r32835;
        double r32837 = tan(r32830);
        double r32838 = r32835 * r32837;
        double r32839 = r32836 * r32838;
        double r32840 = r32834 * r32839;
        double r32841 = r32830 - r32840;
        return r32841;
}

Error

Bits error versus F

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.9

    \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt16.9

    \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]

  4. Applied times-frac16.9

    \[\leadsto \pi \cdot \ell - \color{blue}{\left(\frac{\sqrt{1}}{F} \cdot \frac{\sqrt{1}}{F}\right)} \cdot \tan \left(\pi \cdot \ell\right)\]

  5. Applied associate-*l*12.7

    \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\sqrt{1}}{F} \cdot \left(\frac{\sqrt{1}}{F} \cdot \tan \left(\pi \cdot \ell\right)\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt12.9

    \[\leadsto \pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \sqrt[3]{\frac{\sqrt{1}}{F}}\right) \cdot \sqrt[3]{\frac{\sqrt{1}}{F}}\right)} \cdot \tan \left(\pi \cdot \ell\right)\right)\]

  8. Applied associate-*l*12.9

    \[\leadsto \pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \sqrt[3]{\frac{\sqrt{1}}{F}}\right) \cdot \left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)}\]

  9. Final simplification12.9

    \[\leadsto \pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \sqrt[3]{\frac{\sqrt{1}}{F}}\right) \cdot \left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)\]

Reproduce

herbie shell --seed 2019325 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))