Average Error: 8.6 → 0.7
Time: 40.8s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F} \cdot \frac{1}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F} \cdot \frac{1}{F}
double f(double F, double l) {
        double r615788 = atan2(1.0, 0.0);
        double r615789 = l;
        double r615790 = r615788 * r615789;
        double r615791 = 1.0;
        double r615792 = F;
        double r615793 = r615792 * r615792;
        double r615794 = r615791 / r615793;
        double r615795 = tan(r615790);
        double r615796 = r615794 * r615795;
        double r615797 = r615790 - r615796;
        return r615797;
}
↓
double f(double F, double l) {
        double r615798 = atan2(1.0, 0.0);
        double r615799 = l;
        double r615800 = r615798 * r615799;
        double r615801 = tan(r615800);
        double r615802 = F;
        double r615803 = r615801 / r615802;
        double r615804 = 1.0;
        double r615805 = r615804 / r615802;
        double r615806 = r615803 * r615805;
        double r615807 = r615800 - r615806;
        return r615807;
}

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 8.6

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

  2. Simplified8.1

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

  4. Applied *-un-lft-identity8.1

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

  5. Applied times-frac0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019128 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))