Average Error: 8.4 → 0.7
Time: 38.5s
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 r696356 = atan2(1.0, 0.0);
        double r696357 = l;
        double r696358 = r696356 * r696357;
        double r696359 = 1.0;
        double r696360 = F;
        double r696361 = r696360 * r696360;
        double r696362 = r696359 / r696361;
        double r696363 = tan(r696358);
        double r696364 = r696362 * r696363;
        double r696365 = r696358 - r696364;
        return r696365;
}
↓
double f(double F, double l) {
        double r696366 = atan2(1.0, 0.0);
        double r696367 = l;
        double r696368 = r696366 * r696367;
        double r696369 = 1.0;
        double r696370 = F;
        double r696371 = tan(r696368);
        double r696372 = r696370 / r696371;
        double r696373 = r696369 / r696372;
        double r696374 = r696373 / r696370;
        double r696375 = r696368 - r696374;
        return r696375;
}

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. Simplified7.9

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

  4. Applied associate-/r*0.7

    \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
  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 2019134 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))