Average Error: 19.6 → 1.2
Time: 17.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}} \cdot \left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right| \cdot c0\right)\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}} \cdot \left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right| \cdot c0\right)
double f(double c0, double A, double V, double l) {
        double r100634 = c0;
        double r100635 = A;
        double r100636 = V;
        double r100637 = l;
        double r100638 = r100636 * r100637;
        double r100639 = r100635 / r100638;
        double r100640 = sqrt(r100639);
        double r100641 = r100634 * r100640;
        return r100641;
}
↓
double f(double c0, double A, double V, double l) {
        double r100642 = A;
        double r100643 = cbrt(r100642);
        double r100644 = l;
        double r100645 = cbrt(r100644);
        double r100646 = r100643 / r100645;
        double r100647 = V;
        double r100648 = cbrt(r100647);
        double r100649 = r100646 / r100648;
        double r100650 = sqrt(r100649);
        double r100651 = fabs(r100649);
        double r100652 = c0;
        double r100653 = r100651 * r100652;
        double r100654 = r100650 * r100653;
        return r100654;
}

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 19.6

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

  3. Applied add-cube-cbrt20.0

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

  4. Applied times-frac18.7

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt18.9

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

  8. Applied pow118.9

    \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \color{blue}{{\left(\frac{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\ell}\right)}^{1}}}\]

  9. Applied pow118.9

    \[\leadsto c0 \cdot \sqrt{\color{blue}{{\left(\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}\right)}^{1}} \cdot {\left(\frac{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\ell}\right)}^{1}}\]

  10. Applied pow-prod-down18.9

    \[\leadsto c0 \cdot \sqrt{\color{blue}{{\left(\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\ell}\right)}^{1}}}\]

  11. Simplified19.5

    \[\leadsto c0 \cdot \sqrt{{\color{blue}{\left(\frac{\frac{A}{\ell}}{V}\right)}}^{1}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt19.9

    \[\leadsto c0 \cdot \sqrt{{\left(\frac{\frac{A}{\ell}}{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}\right)}^{1}}\]

  14. Applied add-cube-cbrt20.0

    \[\leadsto c0 \cdot \sqrt{{\left(\frac{\frac{A}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}\right)}^{1}}\]

  15. Applied add-cube-cbrt20.1

    \[\leadsto c0 \cdot \sqrt{{\left(\frac{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}\right)}^{1}}\]

  16. Applied times-frac20.1

    \[\leadsto c0 \cdot \sqrt{{\left(\frac{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}\right)}^{1}}\]

  17. Applied times-frac15.9

    \[\leadsto c0 \cdot \sqrt{{\color{blue}{\left(\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right)}}^{1}}\]

  18. Applied unpow-prod-down15.9

    \[\leadsto c0 \cdot \sqrt{\color{blue}{{\left(\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}\right)}^{1} \cdot {\left(\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right)}^{1}}}\]

  19. Applied sqrt-prod7.4

    \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{{\left(\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}\right)}^{1}} \cdot \sqrt{{\left(\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right)}^{1}}\right)}\]

  20. Applied associate-*r*7.4

    \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{{\left(\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}\right)}^{1}}\right) \cdot \sqrt{{\left(\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right)}^{1}}}\]

  21. Simplified1.2

    \[\leadsto \color{blue}{\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right| \cdot c0\right)} \cdot \sqrt{{\left(\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}{\sqrt[3]{V}}\right)}^{1}}\]

  22. Final simplification1.2

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

Reproduce

herbie shell --seed 2019235 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))