Average Error: 16.8 → 12.7
Time: 30.6s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\left(\sqrt[3]{\frac{\sqrt{1}}{F}} \cdot \sqrt[3]{\frac{\sqrt{1}}{F}}\right) \cdot \left(\frac{\sqrt[3]{\sqrt{1}}}{\sqrt[3]{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)\]
\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(\frac{\sqrt[3]{\sqrt{1}}}{\sqrt[3]{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)
double f(double F, double l) {
        double r2319707 = atan2(1.0, 0.0);
        double r2319708 = l;
        double r2319709 = r2319707 * r2319708;
        double r2319710 = 1.0;
        double r2319711 = F;
        double r2319712 = r2319711 * r2319711;
        double r2319713 = r2319710 / r2319712;
        double r2319714 = tan(r2319709);
        double r2319715 = r2319713 * r2319714;
        double r2319716 = r2319709 - r2319715;
        return r2319716;
}
↓
double f(double F, double l) {
        double r2319717 = atan2(1.0, 0.0);
        double r2319718 = l;
        double r2319719 = r2319717 * r2319718;
        double r2319720 = 1.0;
        double r2319721 = sqrt(r2319720);
        double r2319722 = F;
        double r2319723 = r2319721 / r2319722;
        double r2319724 = cbrt(r2319723);
        double r2319725 = r2319724 * r2319724;
        double r2319726 = cbrt(r2319721);
        double r2319727 = cbrt(r2319722);
        double r2319728 = r2319726 / r2319727;
        double r2319729 = tan(r2319719);
        double r2319730 = r2319728 * r2319729;
        double r2319731 = r2319725 * r2319730;
        double r2319732 = r2319723 * r2319731;
        double r2319733 = r2319719 - r2319732;
        return r2319733;
}

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 16.8

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

  3. Applied add-sqr-sqrt16.8

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

  4. Applied times-frac16.8

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

  5. Applied associate-*l*12.6

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

  7. Applied add-cube-cbrt12.7

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

  8. Applied associate-*l*12.7

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

  10. Applied cbrt-div12.7

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

  11. Final simplification12.7

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

Reproduce

herbie shell --seed 2019173 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))