Average Error: 8.4 → 0.7
Time: 39.3s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right) \cdot \frac{1}{F}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right) \cdot \frac{1}{F}}{F}
double f(double F, double l) {
        double r572901 = atan2(1.0, 0.0);
        double r572902 = l;
        double r572903 = r572901 * r572902;
        double r572904 = 1.0;
        double r572905 = F;
        double r572906 = r572905 * r572905;
        double r572907 = r572904 / r572906;
        double r572908 = tan(r572903);
        double r572909 = r572907 * r572908;
        double r572910 = r572903 - r572909;
        return r572910;
}
↓
double f(double F, double l) {
        double r572911 = atan2(1.0, 0.0);
        double r572912 = l;
        double r572913 = r572911 * r572912;
        double r572914 = tan(r572913);
        double r572915 = 1.0;
        double r572916 = F;
        double r572917 = r572915 / r572916;
        double r572918 = r572914 * r572917;
        double r572919 = r572918 / r572916;
        double r572920 = r572913 - r572919;
        return r572920;
}

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 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 div-inv0.7

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

  7. Final simplification0.7

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

Reproduce

herbie shell --seed 2019124 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))