Average Error: 17.0 → 12.9
Time: 28.7s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\tan \left(\sqrt{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}} \cdot \left(\left(\sqrt{\pi} \cdot \ell\right) \cdot \sqrt{\sqrt[3]{\pi}}\right)\right) \cdot \frac{\sqrt{1}}{F}\right)\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\tan \left(\sqrt{\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}} \cdot \left(\left(\sqrt{\pi} \cdot \ell\right) \cdot \sqrt{\sqrt[3]{\pi}}\right)\right) \cdot \frac{\sqrt{1}}{F}\right)
double f(double F, double l) {
        double r952522 = atan2(1.0, 0.0);
        double r952523 = l;
        double r952524 = r952522 * r952523;
        double r952525 = 1.0;
        double r952526 = F;
        double r952527 = r952526 * r952526;
        double r952528 = r952525 / r952527;
        double r952529 = tan(r952524);
        double r952530 = r952528 * r952529;
        double r952531 = r952524 - r952530;
        return r952531;
}
↓
double f(double F, double l) {
        double r952532 = atan2(1.0, 0.0);
        double r952533 = l;
        double r952534 = r952532 * r952533;
        double r952535 = 1.0;
        double r952536 = sqrt(r952535);
        double r952537 = F;
        double r952538 = r952536 / r952537;
        double r952539 = cbrt(r952532);
        double r952540 = r952539 * r952539;
        double r952541 = sqrt(r952540);
        double r952542 = sqrt(r952532);
        double r952543 = r952542 * r952533;
        double r952544 = sqrt(r952539);
        double r952545 = r952543 * r952544;
        double r952546 = r952541 * r952545;
        double r952547 = tan(r952546);
        double r952548 = r952547 * r952538;
        double r952549 = r952538 * r952548;
        double r952550 = r952534 - r952549;
        return r952550;
}

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 17.0

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

  3. Applied add-sqr-sqrt17.0

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

  4. Applied times-frac17.0

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

  5. Applied associate-*l*12.8

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

  7. Applied add-sqr-sqrt12.9

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

  8. Applied associate-*l*12.9

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

  10. Applied add-cube-cbrt13.0

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

  11. Applied sqrt-prod12.9

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

  12. Applied associate-*l*12.9

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

  13. Final simplification12.9

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

Reproduce

herbie shell --seed 2019169 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))