Average Error: 18.6 → 11.9
Time: 50.1s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.9346483583564717 \cdot 10^{+283}:\\ \;\;\;\;\sqrt{\frac{1}{\ell \cdot V}} \cdot \left(\sqrt{A} \cdot c0\right)\\ \mathbf{if}\;\frac{A}{V} \le -5.980412468850029 \cdot 10^{-41}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\sqrt[3]{\frac{A}{V}} \cdot \sqrt[3]{\frac{A}{V}}}{\frac{\ell}{\sqrt[3]{\frac{A}{V}}}}}\\ \mathbf{if}\;\frac{A}{V} \le 7.463286828776234 \cdot 10^{-299} \lor \neg \left(\frac{A}{V} \le 5.904908779138337 \cdot 10^{+302}\right):\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \end{array}\]

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

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Derivation

  1. Split input into 4 regimes

  2. if (/ A V) < -2.9346483583564717e+283

    1. Initial program 33.7

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

    3. Applied div-inv33.7

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

    4. Applied sqrt-prod39.8

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

    5. Applied associate-*r*39.9

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

    if -2.9346483583564717e+283 < (/ A V) < -5.980412468850029e-41

    1. Initial program 15.9

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

    3. Applied associate-/r*8.9

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

    5. Applied add-cube-cbrt9.3

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

    6. Applied associate-/l*9.3

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

    if -5.980412468850029e-41 < (/ A V) < 7.463286828776234e-299 or 5.904908779138337e+302 < (/ A V)

    1. Initial program 21.1

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

    3. Applied add-sqr-sqrt21.1

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

    4. Applied sqrt-prod21.3

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

    5. Applied associate-*r*21.3

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

    if 7.463286828776234e-299 < (/ A V) < 5.904908779138337e+302

    1. Initial program 15.4

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

    3. Applied associate-/r*9.8

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

    5. Applied sqrt-div0.4

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

  4. Applied simplify11.9

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.9346483583564717 \cdot 10^{+283}:\\ \;\;\;\;\sqrt{\frac{1}{\ell \cdot V}} \cdot \left(\sqrt{A} \cdot c0\right)\\ \mathbf{if}\;\frac{A}{V} \le -5.980412468850029 \cdot 10^{-41}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\sqrt[3]{\frac{A}{V}} \cdot \sqrt[3]{\frac{A}{V}}}{\frac{\ell}{\sqrt[3]{\frac{A}{V}}}}}\\ \mathbf{if}\;\frac{A}{V} \le 7.463286828776234 \cdot 10^{-299} \lor \neg \left(\frac{A}{V} \le 5.904908779138337 \cdot 10^{+302}\right):\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \end{array}}\]

Runtime

Time bar (total: 50.1s)Debug logProfile

herbie shell --seed 2018178 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))