Average Error: 8.5 → 0.7
Time: 39.3s
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 r428345 = atan2(1.0, 0.0);
        double r428346 = l;
        double r428347 = r428345 * r428346;
        double r428348 = 1.0;
        double r428349 = F;
        double r428350 = r428349 * r428349;
        double r428351 = r428348 / r428350;
        double r428352 = tan(r428347);
        double r428353 = r428351 * r428352;
        double r428354 = r428347 - r428353;
        return r428354;
}
↓
double f(double F, double l) {
        double r428355 = atan2(1.0, 0.0);
        double r428356 = l;
        double r428357 = r428355 * r428356;
        double r428358 = 1.0;
        double r428359 = F;
        double r428360 = r428358 / r428359;
        double r428361 = tan(r428357);
        double r428362 = r428358 / r428361;
        double r428363 = r428360 / r428362;
        double r428364 = r428363 / r428359;
        double r428365 = r428357 - r428364;
        return r428365;
}

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. Simplified0.7

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

  4. Applied *-un-lft-identity0.7

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

  5. Applied associate-/l*0.7

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

  7. Applied div-inv0.7

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

  8. Applied associate-/r*0.7

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

  9. 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 2019142 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))