Average Error: 8.4 → 1.0
Time: 44.9s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \left(\sqrt[3]{\frac{1}{F}} \cdot \sqrt[3]{\frac{1}{F}}\right) \cdot \left(\frac{\tan \left(\pi \cdot \ell\right)}{F} \cdot \sqrt[3]{\frac{1}{F}}\right)\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \left(\sqrt[3]{\frac{1}{F}} \cdot \sqrt[3]{\frac{1}{F}}\right) \cdot \left(\frac{\tan \left(\pi \cdot \ell\right)}{F} \cdot \sqrt[3]{\frac{1}{F}}\right)
double f(double F, double l) {
        double r697371 = atan2(1.0, 0.0);
        double r697372 = l;
        double r697373 = r697371 * r697372;
        double r697374 = 1.0;
        double r697375 = F;
        double r697376 = r697375 * r697375;
        double r697377 = r697374 / r697376;
        double r697378 = tan(r697373);
        double r697379 = r697377 * r697378;
        double r697380 = r697373 - r697379;
        return r697380;
}
↓
double f(double F, double l) {
        double r697381 = atan2(1.0, 0.0);
        double r697382 = l;
        double r697383 = r697381 * r697382;
        double r697384 = 1.0;
        double r697385 = F;
        double r697386 = r697384 / r697385;
        double r697387 = cbrt(r697386);
        double r697388 = r697387 * r697387;
        double r697389 = tan(r697383);
        double r697390 = r697389 / r697385;
        double r697391 = r697390 * r697387;
        double r697392 = r697388 * r697391;
        double r697393 = r697383 - r697392;
        return r697393;
}

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 8.4

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

  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 *-un-lft-identity8.0

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

  5. Applied times-frac0.7

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

  7. Applied add-cube-cbrt1.0

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

  8. Applied associate-*l*1.0

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2019104 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))