Average Error: 16.5 → 12.6
Time: 41.7s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\ell \cdot \pi - \left(\tan \left(\sqrt[3]{\ell} \cdot \left(\pi \cdot \left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)\right)\right) \cdot \frac{\sqrt{1}}{F}\right) \cdot \frac{\sqrt{1}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\ell \cdot \pi - \left(\tan \left(\sqrt[3]{\ell} \cdot \left(\pi \cdot \left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right)\right)\right) \cdot \frac{\sqrt{1}}{F}\right) \cdot \frac{\sqrt{1}}{F}
double f(double F, double l) {
        double r965676 = atan2(1.0, 0.0);
        double r965677 = l;
        double r965678 = r965676 * r965677;
        double r965679 = 1.0;
        double r965680 = F;
        double r965681 = r965680 * r965680;
        double r965682 = r965679 / r965681;
        double r965683 = tan(r965678);
        double r965684 = r965682 * r965683;
        double r965685 = r965678 - r965684;
        return r965685;
}
↓
double f(double F, double l) {
        double r965686 = l;
        double r965687 = atan2(1.0, 0.0);
        double r965688 = r965686 * r965687;
        double r965689 = cbrt(r965686);
        double r965690 = r965689 * r965689;
        double r965691 = r965687 * r965690;
        double r965692 = r965689 * r965691;
        double r965693 = tan(r965692);
        double r965694 = 1.0;
        double r965695 = sqrt(r965694);
        double r965696 = F;
        double r965697 = r965695 / r965696;
        double r965698 = r965693 * r965697;
        double r965699 = r965698 * r965697;
        double r965700 = r965688 - r965699;
        return r965700;
}

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 16.5

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

  3. Applied add-sqr-sqrt16.5

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

  4. Applied times-frac16.5

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

  5. Applied associate-*l*12.4

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

  7. Applied add-cube-cbrt12.5

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

  8. Applied associate-*r*12.6

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

  9. Final simplification12.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))