Average Error: 18.7 → 14.8
Time: 25.0s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \le 6.2079968719386 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}} \cdot \left(\sqrt{\left|\sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right| \cdot \sqrt{\sqrt[3]{\frac{\frac{A}{V}}{\ell}}}} \cdot c0\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if l < 6.2079968719386e-310

    1. Initial program 19.1

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]

    2. Initial simplification19.0

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

    4. Applied add-sqr-sqrt19.0

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

    5. Applied sqrt-prod19.2

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

    6. Applied associate-*r*19.2

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

    8. Applied div-inv19.2

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

    10. Applied add-cube-cbrt19.3

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

    11. Applied sqrt-prod19.2

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

    12. Simplified19.2

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

    if 6.2079968719386e-310 < l

    1. Initial program 18.4

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]

    2. Initial simplification17.5

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

    4. Applied sqrt-div10.3

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification14.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le 6.2079968719386 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}} \cdot \left(\sqrt{\left|\sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right| \cdot \sqrt{\sqrt[3]{\frac{\frac{A}{V}}{\ell}}}} \cdot c0\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}\]

Runtime

Time bar (total: 25.0s)Debug logProfile

herbie shell --seed 2018242 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))