Average Error: 16.1 → 11.9
Time: 8.4s
Precision: binary64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right) \cdot 1}{F}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right) \cdot 1}{F}}{F}
(FPCore (F l)
 :precision binary64
 (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))
↓
(FPCore (F l)
 :precision binary64
 (- (* PI l) (/ (/ (* (tan (* PI l)) 1.0) F) F)))
double code(double F, double l) {
	return ((double) (((double) (((double) M_PI) * l)) - ((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) tan(((double) (((double) M_PI) * l)))) * 1.0)) / F) / 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 16.1

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

  3. Applied *-un-lft-identity_binary6416.1

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

  4. Applied times-frac_binary6416.1

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

  5. Applied associate-*l*_binary6412.0

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

  6. Simplified12.0

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

  8. Applied associate-*r/_binary6411.9

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

  10. Applied associate-*r/_binary6411.9

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

  11. Simplified11.9

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

  12. Final simplification11.9

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

Reproduce

herbie shell --seed 2020204 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))