Average Error: 16.8 → 12.8
Time: 9.1s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}{\frac{F}{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\frac{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}{\frac{F}{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}}}{F}
double code(double F, double l) {
	return ((double) (((double) (((double) M_PI) * l)) - ((double) (((double) (1.0 / ((double) (F * F)))) * ((double) tan(((double) (((double) M_PI) * l))))))));
}
↓
double code(double F, double l) {
	return ((double) (((double) (((double) M_PI) * l)) - ((double) (((double) (((double) (((double) cbrt(((double) (1.0 * ((double) tan(((double) (((double) M_PI) * l)))))))) * ((double) cbrt(((double) (1.0 * ((double) tan(((double) (((double) M_PI) * l)))))))))) / ((double) (F / ((double) cbrt(((double) (1.0 * ((double) tan(((double) (((double) M_PI) * l)))))))))))) / F))));
}

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 16.8

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

  3. Applied associate-/r*16.8

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

  4. Applied associate-*l/12.6

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

  5. Simplified12.6

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

  7. Applied add-cube-cbrt12.8

    \[\leadsto \pi \cdot \ell - \frac{\frac{\color{blue}{\left(\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}\right) \cdot \sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}}{F}}{F}\]

  8. Applied associate-/l*12.8

    \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\frac{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}{\frac{F}{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}}}}{F}\]

  9. Final simplification12.8

    \[\leadsto \pi \cdot \ell - \frac{\frac{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)} \cdot \sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}{\frac{F}{\sqrt[3]{1 \cdot \tan \left(\pi \cdot \ell\right)}}}}{F}\]

Reproduce

herbie shell --seed 2020114 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))