Average Error: 16.8 → 12.7
Time: 25.3s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \left(\frac{1}{\sqrt[3]{F} \cdot \sqrt[3]{F}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right) \cdot \frac{\sqrt{1}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \left(\frac{1}{\sqrt[3]{F} \cdot \sqrt[3]{F}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{F}} \cdot \tan \left(\pi \cdot \ell\right)\right)\right) \cdot \frac{\sqrt{1}}{F}
double f(double F, double l) {
        double r810600 = atan2(1.0, 0.0);
        double r810601 = l;
        double r810602 = r810600 * r810601;
        double r810603 = 1.0;
        double r810604 = F;
        double r810605 = r810604 * r810604;
        double r810606 = r810603 / r810605;
        double r810607 = tan(r810602);
        double r810608 = r810606 * r810607;
        double r810609 = r810602 - r810608;
        return r810609;
}
↓
double f(double F, double l) {
        double r810610 = atan2(1.0, 0.0);
        double r810611 = l;
        double r810612 = r810610 * r810611;
        double r810613 = 1.0;
        double r810614 = F;
        double r810615 = cbrt(r810614);
        double r810616 = r810615 * r810615;
        double r810617 = r810613 / r810616;
        double r810618 = 1.0;
        double r810619 = sqrt(r810618);
        double r810620 = r810619 / r810615;
        double r810621 = tan(r810612);
        double r810622 = r810620 * r810621;
        double r810623 = r810617 * r810622;
        double r810624 = r810619 / r810614;
        double r810625 = r810623 * r810624;
        double r810626 = r810612 - r810625;
        return r810626;
}

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-frac16.9

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

  5. Applied associate-*l*12.5

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

  7. Applied add-cube-cbrt12.7

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

  8. Applied *-un-lft-identity12.7

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

  9. Applied times-frac12.7

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

  10. Applied associate-*l*12.7

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

  11. Final simplification12.7

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

Reproduce

herbie shell --seed 2019192 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))