Average Error: 8.5 → 1.1
Time: 41.9s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{\sqrt[3]{\tan \left(\pi \cdot \ell\right)}}{F} \cdot \left(\sqrt[3]{\tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\right)}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\frac{\sqrt[3]{\tan \left(\pi \cdot \ell\right)}}{F} \cdot \left(\sqrt[3]{\tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{\tan \left(\pi \cdot \ell\right)}\right)}{F}
double f(double F, double l) {
        double r686881 = atan2(1.0, 0.0);
        double r686882 = l;
        double r686883 = r686881 * r686882;
        double r686884 = 1.0;
        double r686885 = F;
        double r686886 = r686885 * r686885;
        double r686887 = r686884 / r686886;
        double r686888 = tan(r686883);
        double r686889 = r686887 * r686888;
        double r686890 = r686883 - r686889;
        return r686890;
}
↓
double f(double F, double l) {
        double r686891 = atan2(1.0, 0.0);
        double r686892 = l;
        double r686893 = r686891 * r686892;
        double r686894 = tan(r686893);
        double r686895 = cbrt(r686894);
        double r686896 = F;
        double r686897 = r686895 / r686896;
        double r686898 = r686895 * r686895;
        double r686899 = r686897 * r686898;
        double r686900 = r686899 / r686896;
        double r686901 = r686893 - r686900;
        return r686901;
}

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 8.5

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

  2. Simplified0.6

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

  4. Applied *-un-lft-identity0.6

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

  5. Applied add-cube-cbrt1.1

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

  6. Applied times-frac1.1

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

  7. Simplified1.1

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

  8. Final simplification1.1

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

Reproduce

herbie shell --seed 2019139 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))