Average Error: 15.7 → 12.0
Time: 34.4s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\frac{1}{F} \cdot \tan \left(\left(\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}\right) \cdot \left(\sqrt{\pi} \cdot \ell\right)\right)}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\frac{1}{F} \cdot \tan \left(\left(\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}\right) \cdot \left(\sqrt{\pi} \cdot \ell\right)\right)}{F}
double f(double F, double l) {
        double r657172 = atan2(1.0, 0.0);
        double r657173 = l;
        double r657174 = r657172 * r657173;
        double r657175 = 1.0;
        double r657176 = F;
        double r657177 = r657176 * r657176;
        double r657178 = r657175 / r657177;
        double r657179 = tan(r657174);
        double r657180 = r657178 * r657179;
        double r657181 = r657174 - r657180;
        return r657181;
}
↓
double f(double F, double l) {
        double r657182 = atan2(1.0, 0.0);
        double r657183 = l;
        double r657184 = r657182 * r657183;
        double r657185 = 1.0;
        double r657186 = F;
        double r657187 = r657185 / r657186;
        double r657188 = sqrt(r657182);
        double r657189 = sqrt(r657188);
        double r657190 = r657189 * r657189;
        double r657191 = r657188 * r657183;
        double r657192 = r657190 * r657191;
        double r657193 = tan(r657192);
        double r657194 = r657187 * r657193;
        double r657195 = r657194 / r657186;
        double r657196 = r657184 - r657195;
        return r657196;
}

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 15.7

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

  2. Simplified11.9

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

  4. Applied div-inv12.0

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

  6. Applied add-sqr-sqrt12.1

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

  7. Applied associate-*l*12.1

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

  9. Applied add-sqr-sqrt12.0

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

  10. Final simplification12.0

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

Reproduce

herbie shell --seed 2019143 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))