Average Error: 8.5 → 0.9
Time: 43.8s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{1}{F} \cdot \tan \left(\sqrt{\pi} \cdot \left(\sqrt{\pi} \cdot \ell\right)\right)}{F}\]
\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(\sqrt{\pi} \cdot \left(\sqrt{\pi} \cdot \ell\right)\right)}{F}
double f(double F, double l) {
        double r792868 = atan2(1.0, 0.0);
        double r792869 = l;
        double r792870 = r792868 * r792869;
        double r792871 = 1.0;
        double r792872 = F;
        double r792873 = r792872 * r792872;
        double r792874 = r792871 / r792873;
        double r792875 = tan(r792870);
        double r792876 = r792874 * r792875;
        double r792877 = r792870 - r792876;
        return r792877;
}
↓
double f(double F, double l) {
        double r792878 = atan2(1.0, 0.0);
        double r792879 = l;
        double r792880 = r792878 * r792879;
        double r792881 = 1.0;
        double r792882 = F;
        double r792883 = r792881 / r792882;
        double r792884 = sqrt(r792878);
        double r792885 = r792884 * r792879;
        double r792886 = r792884 * r792885;
        double r792887 = tan(r792886);
        double r792888 = r792883 * r792887;
        double r792889 = r792888 / r792882;
        double r792890 = r792880 - r792889;
        return r792890;
}

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 8.5

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

  2. Simplified0.6

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

  4. Applied div-inv0.6

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

  6. Applied add-sqr-sqrt0.9

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

  7. Applied associate-*l*0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019141 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))