Average Error: 16.6 → 12.4
Time: 28.0s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\sqrt{1}}{\frac{F}{\tan \left(\pi \cdot \ell\right)}} \cdot \frac{\sqrt{1}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\sqrt{1}}{\frac{F}{\tan \left(\pi \cdot \ell\right)}} \cdot \frac{\sqrt{1}}{F}
double f(double F, double l) {
        double r1004772 = atan2(1.0, 0.0);
        double r1004773 = l;
        double r1004774 = r1004772 * r1004773;
        double r1004775 = 1.0;
        double r1004776 = F;
        double r1004777 = r1004776 * r1004776;
        double r1004778 = r1004775 / r1004777;
        double r1004779 = tan(r1004774);
        double r1004780 = r1004778 * r1004779;
        double r1004781 = r1004774 - r1004780;
        return r1004781;
}
↓
double f(double F, double l) {
        double r1004782 = atan2(1.0, 0.0);
        double r1004783 = l;
        double r1004784 = r1004782 * r1004783;
        double r1004785 = 1.0;
        double r1004786 = sqrt(r1004785);
        double r1004787 = F;
        double r1004788 = tan(r1004784);
        double r1004789 = r1004787 / r1004788;
        double r1004790 = r1004786 / r1004789;
        double r1004791 = r1004786 / r1004787;
        double r1004792 = r1004790 * r1004791;
        double r1004793 = r1004784 - r1004792;
        return r1004793;
}

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 16.6

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

  3. Applied add-sqr-sqrt16.6

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

  4. Applied times-frac16.7

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

  5. Applied associate-*l*12.4

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

  7. Applied associate-*l/12.3

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

  9. Applied associate-/l*12.4

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

  10. Final simplification12.4

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

Reproduce

herbie shell --seed 2019170 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))