Average Error: 8.7 → 0.6
Time: 34.7s
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 r486981 = atan2(1.0, 0.0);
        double r486982 = l;
        double r486983 = r486981 * r486982;
        double r486984 = 1.0;
        double r486985 = F;
        double r486986 = r486985 * r486985;
        double r486987 = r486984 / r486986;
        double r486988 = tan(r486983);
        double r486989 = r486987 * r486988;
        double r486990 = r486983 - r486989;
        return r486990;
}
↓
double f(double F, double l) {
        double r486991 = atan2(1.0, 0.0);
        double r486992 = l;
        double r486993 = r486991 * r486992;
        double r486994 = 1.0;
        double r486995 = F;
        double r486996 = tan(r486993);
        double r486997 = r486995 / r486996;
        double r486998 = r486994 / r486997;
        double r486999 = r486998 / r486995;
        double r487000 = r486993 - r486999;
        return r487000;
}

Error

Bits error versus F

Bits error versus l

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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 *-un-lft-identity0.6

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

  7. Applied associate-/l*0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019135 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))