Average Error: 16.6 → 12.1
Time: 8.9s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{1}{F \cdot 1} \cdot \frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{1}{F \cdot 1} \cdot \frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F}
double code(double F, double l) {
	return ((((double) M_PI) * l) - ((1.0 / (F * F)) * tan((((double) M_PI) * l))));
}
↓
double code(double F, double l) {
	return ((((double) M_PI) * l) - ((1.0 / (F * 1.0)) * ((1.0 * tan((((double) M_PI) * l))) / F)));
}

Error

Bits error versus F

Bits error versus l

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.6

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

  3. Applied *-un-lft-identity16.6

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

  4. Applied associate-*r*16.6

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

  5. Applied *-un-lft-identity16.6

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

  6. Applied times-frac16.6

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

  7. Applied associate-*l*12.1

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

  8. Simplified12.1

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

  9. Final simplification12.1

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

Reproduce

herbie shell --seed 2020066 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))