Average Error: 18.7 → 12.4
Time: 33.5s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{V \cdot \ell} \le -4.3182281409439046 \cdot 10^{+305}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt[3]{\frac{\frac{A}{V}}{\ell}}}\right) \cdot \left|\sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right|\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le -3.816355223225376 \cdot 10^{-133}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le 7.889884570616071 \cdot 10^{-304}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]

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 4 regimes

  2. if (/ 1 (* V l)) < -4.3182281409439046e+305

    1. Initial program 58.0

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

    3. Applied add-cube-cbrt58.0

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

    4. Applied sqrt-prod58.0

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

    5. Applied associate-*r*58.0

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

    6. Applied simplify58.0

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

    7. Taylor expanded around 0 62.3

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

    8. Applied simplify35.4

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

    if -4.3182281409439046e+305 < (/ 1 (* V l)) < -3.816355223225376e-133

    1. Initial program 8.5

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

    if -3.816355223225376e-133 < (/ 1 (* V l)) < 7.889884570616071e-304

    1. Initial program 28.8

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

    3. Applied associate-/r*19.1

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

    if 7.889884570616071e-304 < (/ 1 (* V l))

    1. Initial program 15.2

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

    3. Applied sqrt-div6.5

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

    4. Applied associate-*r/8.6

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

Runtime

Time bar (total: 33.5s)Debug logProfile

herbie shell --seed 2019053 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))