Average Error: 8.5 → 0.6
Time: 44.4s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right) \cdot \frac{1}{F}}{F}\]
\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) \cdot \frac{1}{F}}{F}
double f(double F, double l) {
        double r769744 = atan2(1.0, 0.0);
        double r769745 = l;
        double r769746 = r769744 * r769745;
        double r769747 = 1.0;
        double r769748 = F;
        double r769749 = r769748 * r769748;
        double r769750 = r769747 / r769749;
        double r769751 = tan(r769746);
        double r769752 = r769750 * r769751;
        double r769753 = r769746 - r769752;
        return r769753;
}
↓
double f(double F, double l) {
        double r769754 = atan2(1.0, 0.0);
        double r769755 = l;
        double r769756 = r769754 * r769755;
        double r769757 = tan(r769756);
        double r769758 = 1.0;
        double r769759 = F;
        double r769760 = r769758 / r769759;
        double r769761 = r769757 * r769760;
        double r769762 = r769761 / r769759;
        double r769763 = r769756 - r769762;
        return r769763;
}

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 div-inv0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))