Average Error: 8.7 → 0.7
Time: 47.4s
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 r731434 = atan2(1.0, 0.0);
        double r731435 = l;
        double r731436 = r731434 * r731435;
        double r731437 = 1.0;
        double r731438 = F;
        double r731439 = r731438 * r731438;
        double r731440 = r731437 / r731439;
        double r731441 = tan(r731436);
        double r731442 = r731440 * r731441;
        double r731443 = r731436 - r731442;
        return r731443;
}
↓
double f(double F, double l) {
        double r731444 = atan2(1.0, 0.0);
        double r731445 = l;
        double r731446 = r731444 * r731445;
        double r731447 = 1.0;
        double r731448 = F;
        double r731449 = tan(r731446);
        double r731450 = r731448 / r731449;
        double r731451 = r731447 / r731450;
        double r731452 = r731451 / r731448;
        double r731453 = r731446 - r731452;
        return r731453;
}

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-num0.7

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

  7. Final simplification0.7

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

Reproduce

herbie shell --seed 2019125 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))