Average Error: 8.4 → 0.7
Time: 47.0s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{1}{\frac{F}{\frac{\frac{\sin \left(\pi \cdot \ell\right)}{\cos \left(\sqrt[3]{\left(\left(\pi \cdot \ell\right) \cdot \left(\pi \cdot \ell\right)\right) \cdot \left(\pi \cdot \ell\right)}\right)}}{F}}}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{1}{\frac{F}{\frac{\frac{\sin \left(\pi \cdot \ell\right)}{\cos \left(\sqrt[3]{\left(\left(\pi \cdot \ell\right) \cdot \left(\pi \cdot \ell\right)\right) \cdot \left(\pi \cdot \ell\right)}\right)}}{F}}}
double f(double F, double l) {
        double r779198 = atan2(1.0, 0.0);
        double r779199 = l;
        double r779200 = r779198 * r779199;
        double r779201 = 1.0;
        double r779202 = F;
        double r779203 = r779202 * r779202;
        double r779204 = r779201 / r779203;
        double r779205 = tan(r779200);
        double r779206 = r779204 * r779205;
        double r779207 = r779200 - r779206;
        return r779207;
}
↓
double f(double F, double l) {
        double r779208 = atan2(1.0, 0.0);
        double r779209 = l;
        double r779210 = r779208 * r779209;
        double r779211 = 1.0;
        double r779212 = F;
        double r779213 = sin(r779210);
        double r779214 = r779210 * r779210;
        double r779215 = r779214 * r779210;
        double r779216 = cbrt(r779215);
        double r779217 = cos(r779216);
        double r779218 = r779213 / r779217;
        double r779219 = r779218 / r779212;
        double r779220 = r779212 / r779219;
        double r779221 = r779211 / r779220;
        double r779222 = r779210 - r779221;
        return r779222;
}

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 8.4

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

  2. Simplified0.7

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

  4. Applied clear-num0.7

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

  5. Taylor expanded around inf 0.7

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

  7. Applied add-cbrt-cube0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019138 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))