Average Error: 19.2 → 1.3
Time: 21.2s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt[3]{\sqrt[3]{\ell}}}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt[3]{\sqrt[3]{\ell}}}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}
double f(double c0, double A, double V, double l) {
        double r4539800 = c0;
        double r4539801 = A;
        double r4539802 = V;
        double r4539803 = l;
        double r4539804 = r4539802 * r4539803;
        double r4539805 = r4539801 / r4539804;
        double r4539806 = sqrt(r4539805);
        double r4539807 = r4539800 * r4539806;
        return r4539807;
}
↓
double f(double c0, double A, double V, double l) {
        double r4539808 = c0;
        double r4539809 = A;
        double r4539810 = cbrt(r4539809);
        double r4539811 = l;
        double r4539812 = cbrt(r4539811);
        double r4539813 = r4539812 * r4539812;
        double r4539814 = cbrt(r4539813);
        double r4539815 = cbrt(r4539812);
        double r4539816 = r4539814 * r4539815;
        double r4539817 = r4539810 / r4539816;
        double r4539818 = V;
        double r4539819 = cbrt(r4539818);
        double r4539820 = r4539817 / r4539819;
        double r4539821 = fabs(r4539820);
        double r4539822 = r4539808 * r4539821;
        double r4539823 = r4539810 / r4539819;
        double r4539824 = r4539823 / r4539812;
        double r4539825 = sqrt(r4539824);
        double r4539826 = r4539822 * r4539825;
        return r4539826;
}

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 19.2

    \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
  2. Using strategy rm

  3. Applied associate-/r*19.0

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt19.3

    \[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{V}}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}\]

  6. Applied add-cube-cbrt19.4

    \[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\]

  7. Applied add-cube-cbrt19.5

    \[\leadsto c0 \cdot \sqrt{\frac{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\]

  8. Applied times-frac19.5

    \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{V}}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\]

  9. Applied times-frac15.5

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}}\]

  10. Applied sqrt-prod7.3

    \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\right)}\]

  11. Applied associate-*r*7.3

    \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}}\]

  12. Simplified1.1

    \[\leadsto \color{blue}{\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right| \cdot c0\right)} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
  13. Using strategy rm

  14. Applied add-cube-cbrt1.2

    \[\leadsto \left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}}{\sqrt[3]{V}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]

  15. Applied cbrt-prod1.3

    \[\leadsto \left(\left|\frac{\frac{\sqrt[3]{A}}{\color{blue}{\sqrt[3]{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt[3]{\sqrt[3]{\ell}}}}}{\sqrt[3]{V}}\right| \cdot c0\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]

  16. Final simplification1.3

    \[\leadsto \left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt[3]{\sqrt[3]{\ell}}}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))