Average Error: 16.5 → 12.4
Time: 8.0s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\sqrt{1} \cdot \frac{1}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}\right)\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \left(\sqrt{1} \cdot \frac{1}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}\right)
double f(double F, double l) {
        double r16050 = atan2(1.0, 0.0);
        double r16051 = l;
        double r16052 = r16050 * r16051;
        double r16053 = 1.0;
        double r16054 = F;
        double r16055 = r16054 * r16054;
        double r16056 = r16053 / r16055;
        double r16057 = tan(r16052);
        double r16058 = r16056 * r16057;
        double r16059 = r16052 - r16058;
        return r16059;
}
↓
double f(double F, double l) {
        double r16060 = atan2(1.0, 0.0);
        double r16061 = l;
        double r16062 = r16060 * r16061;
        double r16063 = 1.0;
        double r16064 = sqrt(r16063);
        double r16065 = F;
        double r16066 = r16064 / r16065;
        double r16067 = 1.0;
        double r16068 = tan(r16062);
        double r16069 = r16065 / r16068;
        double r16070 = r16067 / r16069;
        double r16071 = r16064 * r16070;
        double r16072 = r16066 * r16071;
        double r16073 = r16062 - r16072;
        return r16073;
}

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 16.5

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

  3. Applied add-sqr-sqrt16.5

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

  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 div-inv12.4

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

  8. Applied associate-*l*12.4

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

  9. Simplified12.4

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

  11. Applied clear-num12.4

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

  12. Final simplification12.4

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

Reproduce

herbie shell --seed 2020065 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))