Average Error: 16.2 → 12.3
Time: 21.5s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{1}{F} \cdot \left(\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)\right)\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{1}{F} \cdot \left(\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)\right)
double f(double F, double l) {
        double r24842 = atan2(1.0, 0.0);
        double r24843 = l;
        double r24844 = r24842 * r24843;
        double r24845 = 1.0;
        double r24846 = F;
        double r24847 = r24846 * r24846;
        double r24848 = r24845 / r24847;
        double r24849 = tan(r24844);
        double r24850 = r24848 * r24849;
        double r24851 = r24844 - r24850;
        return r24851;
}
↓
double f(double F, double l) {
        double r24852 = atan2(1.0, 0.0);
        double r24853 = l;
        double r24854 = r24852 * r24853;
        double r24855 = 1.0;
        double r24856 = F;
        double r24857 = r24855 / r24856;
        double r24858 = 1.0;
        double r24859 = r24858 / r24856;
        double r24860 = tan(r24854);
        double r24861 = r24859 * r24860;
        double r24862 = r24857 * r24861;
        double r24863 = r24854 - r24862;
        return r24863;
}

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 16.2

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

  3. Applied *-un-lft-identity16.2

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

  4. Applied times-frac16.2

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

  5. Applied associate-*l*12.3

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

  6. Final simplification12.3

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

Reproduce

herbie shell --seed 2019209 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))