Average Error: 8.5 → 0.7
Time: 35.5s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{\frac{1}{F}}{\frac{1}{\tan \left(\pi \cdot \ell\right)}}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\frac{\frac{1}{F}}{\frac{1}{\tan \left(\pi \cdot \ell\right)}}}{F}
double f(double F, double l) {
        double r573543 = atan2(1.0, 0.0);
        double r573544 = l;
        double r573545 = r573543 * r573544;
        double r573546 = 1.0;
        double r573547 = F;
        double r573548 = r573547 * r573547;
        double r573549 = r573546 / r573548;
        double r573550 = tan(r573545);
        double r573551 = r573549 * r573550;
        double r573552 = r573545 - r573551;
        return r573552;
}
↓
double f(double F, double l) {
        double r573553 = atan2(1.0, 0.0);
        double r573554 = l;
        double r573555 = r573553 * r573554;
        double r573556 = 1.0;
        double r573557 = F;
        double r573558 = r573556 / r573557;
        double r573559 = tan(r573555);
        double r573560 = r573556 / r573559;
        double r573561 = r573558 / r573560;
        double r573562 = r573561 / r573557;
        double r573563 = r573555 - r573562;
        return r573563;
}

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 8.5

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

  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*0.6

    \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
  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*0.7

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

  9. Applied div-inv0.7

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

  10. Applied associate-/r*0.7

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

  11. Final simplification0.7

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

Reproduce

herbie shell --seed 2019132 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))