Average Error: 16.8 → 12.6
Time: 9.5s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\frac{\sqrt{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{F} \cdot \sqrt[3]{F}} \cdot \left(\frac{\sqrt{\sqrt[3]{1}}}{\sqrt[3]{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\frac{\sqrt{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{F} \cdot \sqrt[3]{F}} \cdot \left(\frac{\sqrt{\sqrt[3]{1}}}{\sqrt[3]{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right)
double f(double F, double l) {
        double r19636 = atan2(1.0, 0.0);
        double r19637 = l;
        double r19638 = r19636 * r19637;
        double r19639 = 1.0;
        double r19640 = F;
        double r19641 = r19640 * r19640;
        double r19642 = r19639 / r19641;
        double r19643 = tan(r19638);
        double r19644 = r19642 * r19643;
        double r19645 = r19638 - r19644;
        return r19645;
}
↓
double f(double F, double l) {
        double r19646 = atan2(1.0, 0.0);
        double r19647 = l;
        double r19648 = r19646 * r19647;
        double r19649 = 1.0;
        double r19650 = sqrt(r19649);
        double r19651 = F;
        double r19652 = r19650 / r19651;
        double r19653 = cbrt(r19649);
        double r19654 = r19653 * r19653;
        double r19655 = sqrt(r19654);
        double r19656 = cbrt(r19651);
        double r19657 = r19656 * r19656;
        double r19658 = r19655 / r19657;
        double r19659 = sqrt(r19653);
        double r19660 = r19659 / r19656;
        double r19661 = tan(r19648);
        double r19662 = r19660 * r19661;
        double r19663 = r19658 * r19662;
        double r19664 = r19652 * r19663;
        double r19665 = r19648 - r19664;
        return r19665;
}

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*12.4

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

  7. Applied add-cube-cbrt12.6

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

  8. Applied add-cube-cbrt12.6

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

  9. Applied sqrt-prod12.6

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

  10. Applied times-frac12.6

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

  11. Applied associate-*l*12.6

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

  12. Final simplification12.6

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

Reproduce

herbie shell --seed 2019346 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))