Average Error: 19.0 → 12.1
Time: 16.5s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.482284671134666 \cdot 10^{-167}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 5.4830150794009595 \cdot 10^{+249}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

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 (* V l) < -2.482284671134666e-167

    1. Initial program 14.1

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

    3. Applied div-inv14.1

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

    if -2.482284671134666e-167 < (* V l) < -0.0

    1. Initial program 43.7

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

    2. Initial simplification29.5

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

    if -0.0 < (* V l) < 5.4830150794009595e+249

    1. Initial program 10.0

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

    3. Applied div-inv10.3

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

    5. Applied un-div-inv10.0

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

    6. Applied sqrt-div0.7

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

    if 5.4830150794009595e+249 < (* V l)

    1. Initial program 32.5

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

    3. Applied div-inv32.5

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

    5. Applied *-un-lft-identity32.5

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

    6. Applied associate-*r*32.5

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

    7. Simplified18.7

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

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.482284671134666 \cdot 10^{-167}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 5.4830150794009595 \cdot 10^{+249}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Runtime

Time bar (total: 16.5s)Debug logProfile

herbie shell --seed 2018254 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))