Average Error: 8.7 → 0.6
Time: 35.1s
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 r424528 = atan2(1.0, 0.0);
        double r424529 = l;
        double r424530 = r424528 * r424529;
        double r424531 = 1.0;
        double r424532 = F;
        double r424533 = r424532 * r424532;
        double r424534 = r424531 / r424533;
        double r424535 = tan(r424530);
        double r424536 = r424534 * r424535;
        double r424537 = r424530 - r424536;
        return r424537;
}
↓
double f(double F, double l) {
        double r424538 = atan2(1.0, 0.0);
        double r424539 = l;
        double r424540 = r424538 * r424539;
        double r424541 = 1.0;
        double r424542 = F;
        double r424543 = tan(r424540);
        double r424544 = r424542 / r424543;
        double r424545 = r424541 / r424544;
        double r424546 = r424545 / r424542;
        double r424547 = r424540 - r424546;
        return r424547;
}

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 8.7

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

  2. Simplified8.2

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

  4. Applied associate-/r*0.6

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

  6. Applied clear-num0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))