Average Error: 18.0 → 14.0
Time: 20.4s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} = -\infty:\\ \;\;\;\;\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\sqrt[3]{\frac{\frac{A}{V}}{\ell}} \cdot \left(\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}} \cdot \sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right)}}\right)\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \le -2.6114392726865727 \cdot 10^{-179}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \le 1.4559650229079849 \cdot 10^{-152}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \le 1.266492294757723 \cdot 10^{+291}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\ell}} \cdot \left(\sqrt{\frac{A}{V}} \cdot c0\right)\\ \end{array}\]

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 (* c0 (sqrt (/ A (* V l)))) < -inf.0

    1. Initial program 60.9

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

    2. Initial simplification46.1

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

    4. Applied add-sqr-sqrt46.1

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

    5. Applied sqrt-prod46.2

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

    6. Applied associate-*r*46.2

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

    8. Applied add-cube-cbrt46.2

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

    10. Applied cbrt-div46.2

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

    if -inf.0 < (* c0 (sqrt (/ A (* V l)))) < -2.6114392726865727e-179 or 1.4559650229079849e-152 < (* c0 (sqrt (/ A (* V l)))) < 1.266492294757723e+291

    1. Initial program 0.7

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

    if -2.6114392726865727e-179 < (* c0 (sqrt (/ A (* V l)))) < 1.4559650229079849e-152

    1. Initial program 24.1

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

    2. Initial simplification19.4

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

    if 1.266492294757723e+291 < (* c0 (sqrt (/ A (* V l))))

    1. Initial program 56.6

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

    2. Initial simplification43.3

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

    4. Applied div-inv43.3

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

    5. Applied sqrt-prod40.9

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

    6. Applied associate-*r*41.6

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\frac{A}{V}}\right) \cdot \sqrt{\frac{1}{\ell}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification14.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} = -\infty:\\ \;\;\;\;\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\sqrt[3]{\frac{\frac{A}{V}}{\ell}} \cdot \left(\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}} \cdot \sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right)}}\right)\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \le -2.6114392726865727 \cdot 10^{-179}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \le 1.4559650229079849 \cdot 10^{-152}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \le 1.266492294757723 \cdot 10^{+291}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\ell}} \cdot \left(\sqrt{\frac{A}{V}} \cdot c0\right)\\ \end{array}\]

Runtime

Time bar (total: 20.4s)Debug logProfile

herbie shell --seed 2018249 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))