Average Error: 8.6 → 0.8
Time: 42.1s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \left(\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)\right) \cdot \frac{1}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \left(\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)\right) \cdot \frac{1}{F}
double f(double F, double l) {
        double r578579 = atan2(1.0, 0.0);
        double r578580 = l;
        double r578581 = r578579 * r578580;
        double r578582 = 1.0;
        double r578583 = F;
        double r578584 = r578583 * r578583;
        double r578585 = r578582 / r578584;
        double r578586 = tan(r578581);
        double r578587 = r578585 * r578586;
        double r578588 = r578581 - r578587;
        return r578588;
}
↓
double f(double F, double l) {
        double r578589 = atan2(1.0, 0.0);
        double r578590 = l;
        double r578591 = r578589 * r578590;
        double r578592 = 1.0;
        double r578593 = F;
        double r578594 = r578592 / r578593;
        double r578595 = tan(r578591);
        double r578596 = r578594 * r578595;
        double r578597 = r578596 * r578594;
        double r578598 = r578591 - r578597;
        return r578598;
}

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. Simplified8.0

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

  4. Applied *-un-lft-identity8.0

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

  5. Applied times-frac0.7

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

  7. Applied div-inv0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019107 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))