Average Error: 18.5 → 11.8
Time: 18.0s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{\ell \cdot V} \le -3.2251725300375785 \cdot 10^{+87}:\\ \;\;\;\;\sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}} \cdot c0\\ \mathbf{elif}\;\frac{1}{\ell \cdot V} \le -5.6514315124297986 \cdot 10^{-219}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right)\\ \mathbf{elif}\;\frac{1}{\ell \cdot V} \le 8.248992030751813 \cdot 10^{-303}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]

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 4 regimes

  2. if (/ 1 (* V l)) < -3.2251725300375785e+87

    1. Initial program 27.9

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

    3. Applied clear-num27.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}}\]
    4. Using strategy rm

    5. Applied associate-/l*23.8

      \[\leadsto c0 \cdot \sqrt{\frac{1}{\color{blue}{\frac{V}{\frac{A}{\ell}}}}}\]

    if -3.2251725300375785e+87 < (/ 1 (* V l)) < -5.6514315124297986e-219

    1. Initial program 5.3

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

    3. Applied add-sqr-sqrt5.3

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

    4. Applied sqrt-prod5.6

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

    5. Applied associate-*r*5.6

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

    if -5.6514315124297986e-219 < (/ 1 (* V l)) < 8.248992030751813e-303

    1. Initial program 35.3

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

    2. Initial simplification21.3

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

    if 8.248992030751813e-303 < (/ 1 (* V l))

    1. Initial program 14.5

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

    3. Applied sqrt-div6.2

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification11.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{\ell \cdot V} \le -3.2251725300375785 \cdot 10^{+87}:\\ \;\;\;\;\sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}} \cdot c0\\ \mathbf{elif}\;\frac{1}{\ell \cdot V} \le -5.6514315124297986 \cdot 10^{-219}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right)\\ \mathbf{elif}\;\frac{1}{\ell \cdot V} \le 8.248992030751813 \cdot 10^{-303}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]

Runtime

Time bar (total: 18.0s)Debug logProfile

herbie shell --seed 2018217 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))