Average Error: 8.4 → 0.7
Time: 41.7s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)}{F}
double f(double F, double l) {
        double r637622 = atan2(1.0, 0.0);
        double r637623 = l;
        double r637624 = r637622 * r637623;
        double r637625 = 1.0;
        double r637626 = F;
        double r637627 = r637626 * r637626;
        double r637628 = r637625 / r637627;
        double r637629 = tan(r637624);
        double r637630 = r637628 * r637629;
        double r637631 = r637624 - r637630;
        return r637631;
}
↓
double f(double F, double l) {
        double r637632 = atan2(1.0, 0.0);
        double r637633 = l;
        double r637634 = r637632 * r637633;
        double r637635 = 1.0;
        double r637636 = F;
        double r637637 = r637635 / r637636;
        double r637638 = tan(r637634);
        double r637639 = r637637 * r637638;
        double r637640 = r637639 / r637636;
        double r637641 = r637634 - r637640;
        return r637641;
}

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. Simplified8.0

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

  4. Applied *-un-lft-identity8.0

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

  5. Applied times-frac0.7

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

  7. Applied associate-*r/0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019121 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))