Average Error: 8.4 → 0.7
Time: 38.1s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{1}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\frac{1}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}}{F}
double f(double F, double l) {
        double r739793 = atan2(1.0, 0.0);
        double r739794 = l;
        double r739795 = r739793 * r739794;
        double r739796 = 1.0;
        double r739797 = F;
        double r739798 = r739797 * r739797;
        double r739799 = r739796 / r739798;
        double r739800 = tan(r739795);
        double r739801 = r739799 * r739800;
        double r739802 = r739795 - r739801;
        return r739802;
}
↓
double f(double F, double l) {
        double r739803 = atan2(1.0, 0.0);
        double r739804 = l;
        double r739805 = r739803 * r739804;
        double r739806 = 1.0;
        double r739807 = F;
        double r739808 = tan(r739805);
        double r739809 = r739807 / r739808;
        double r739810 = r739806 / r739809;
        double r739811 = r739810 / r739807;
        double r739812 = r739805 - r739811;
        return r739812;
}

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 8.4

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

  2. Simplified7.9

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

  4. Applied associate-/r*0.7

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

  6. Applied clear-num0.7

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

  7. Final simplification0.7

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))