Average Error: 16.6 → 12.4
Time: 24.4s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \left(\left(\sqrt[3]{\sqrt{1}} \cdot \sqrt[3]{\sqrt{1}}\right) \cdot \frac{\sqrt[3]{\sqrt{1}}}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}\right) \cdot \frac{\sqrt{1}}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \left(\left(\sqrt[3]{\sqrt{1}} \cdot \sqrt[3]{\sqrt{1}}\right) \cdot \frac{\sqrt[3]{\sqrt{1}}}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}\right) \cdot \frac{\sqrt{1}}{F}
double f(double F, double l) {
        double r858195 = atan2(1.0, 0.0);
        double r858196 = l;
        double r858197 = r858195 * r858196;
        double r858198 = 1.0;
        double r858199 = F;
        double r858200 = r858199 * r858199;
        double r858201 = r858198 / r858200;
        double r858202 = tan(r858197);
        double r858203 = r858201 * r858202;
        double r858204 = r858197 - r858203;
        return r858204;
}
↓
double f(double F, double l) {
        double r858205 = atan2(1.0, 0.0);
        double r858206 = l;
        double r858207 = r858205 * r858206;
        double r858208 = 1.0;
        double r858209 = sqrt(r858208);
        double r858210 = cbrt(r858209);
        double r858211 = r858210 * r858210;
        double r858212 = F;
        double r858213 = tan(r858207);
        double r858214 = r858212 / r858213;
        double r858215 = r858210 / r858214;
        double r858216 = r858211 * r858215;
        double r858217 = r858209 / r858212;
        double r858218 = r858216 * r858217;
        double r858219 = r858207 - r858218;
        return r858219;
}

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 16.6

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

  3. Applied add-sqr-sqrt16.6

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

  4. Applied times-frac16.6

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

  5. Applied associate-*l*12.4

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

  7. Applied add-sqr-sqrt12.5

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

  8. Applied associate-*l*12.5

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

  10. Applied *-un-lft-identity12.5

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

  11. Applied add-cube-cbrt12.5

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

  12. Applied times-frac12.5

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

  13. Applied associate-*l*12.5

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

  14. Simplified12.4

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

  15. Final simplification12.4

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

Reproduce

herbie shell --seed 2019172 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))