Average Error: 8.6 → 0.7
Time: 41.4s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F} \cdot \frac{1}{F}\]
\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)}{F} \cdot \frac{1}{F}
double f(double F, double l) {
        double r670958 = atan2(1.0, 0.0);
        double r670959 = l;
        double r670960 = r670958 * r670959;
        double r670961 = 1.0;
        double r670962 = F;
        double r670963 = r670962 * r670962;
        double r670964 = r670961 / r670963;
        double r670965 = tan(r670960);
        double r670966 = r670964 * r670965;
        double r670967 = r670960 - r670966;
        return r670967;
}
↓
double f(double F, double l) {
        double r670968 = atan2(1.0, 0.0);
        double r670969 = l;
        double r670970 = r670968 * r670969;
        double r670971 = tan(r670970);
        double r670972 = F;
        double r670973 = r670971 / r670972;
        double r670974 = 1.0;
        double r670975 = r670974 / r670972;
        double r670976 = r670973 * r670975;
        double r670977 = r670970 - r670976;
        return r670977;
}

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 8.6

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

  2. Simplified8.1

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

  4. Applied *-un-lft-identity8.1

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

  5. Applied times-frac0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))