Average Error: 8.7 → 0.7
Time: 56.8s
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 r1091527 = atan2(1.0, 0.0);
        double r1091528 = l;
        double r1091529 = r1091527 * r1091528;
        double r1091530 = 1.0;
        double r1091531 = F;
        double r1091532 = r1091531 * r1091531;
        double r1091533 = r1091530 / r1091532;
        double r1091534 = tan(r1091529);
        double r1091535 = r1091533 * r1091534;
        double r1091536 = r1091529 - r1091535;
        return r1091536;
}
↓
double f(double F, double l) {
        double r1091537 = atan2(1.0, 0.0);
        double r1091538 = l;
        double r1091539 = r1091537 * r1091538;
        double r1091540 = tan(r1091539);
        double r1091541 = F;
        double r1091542 = r1091540 / r1091541;
        double r1091543 = 1.0;
        double r1091544 = r1091543 / r1091541;
        double r1091545 = r1091542 * r1091544;
        double r1091546 = r1091539 - r1091545;
        return r1091546;
}

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 *-un-lft-identity8.2

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

  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 2019125 +o rules:numerics
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))