Average Error: 18.6 → 12.4
Time: 35.0s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.004776637139463 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\frac{A}{V} \le -1.3501087918197612 \cdot 10^{-111}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{\ell}{\frac{A}{V}}}}\\ \mathbf{elif}\;\frac{A}{V} \le 9.043080568084718 \cdot 10^{-301}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{1}{\ell}} \cdot \sqrt{\frac{A}{V}}\right) \cdot c0\\ \end{array}\]

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

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/ A V) < -2.004776637139463e+296 or -1.3501087918197612e-111 < (/ A V) < 9.043080568084718e-301

    1. Initial program 22.3

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

    2. Initial simplification33.0

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

    4. Applied *-commutative33.0

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

    6. Applied associate-/l/22.3

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

    if -2.004776637139463e+296 < (/ A V) < -1.3501087918197612e-111

    1. Initial program 15.6

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

    2. Initial simplification8.2

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

    4. Applied *-commutative8.2

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

    6. Applied *-un-lft-identity8.2

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

    7. Applied associate-/l*8.4

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

    if 9.043080568084718e-301 < (/ A V)

    1. Initial program 17.6

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

    2. Initial simplification15.0

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

    4. Applied *-commutative15.0

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

    6. Applied div-inv15.0

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

    7. Applied sqrt-prod7.3

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

  4. Final simplification12.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.004776637139463 \cdot 10^{+296}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\frac{A}{V} \le -1.3501087918197612 \cdot 10^{-111}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{\ell}{\frac{A}{V}}}}\\ \mathbf{elif}\;\frac{A}{V} \le 9.043080568084718 \cdot 10^{-301}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{1}{\ell}} \cdot \sqrt{\frac{A}{V}}\right) \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 35.0s)Debug logProfile

herbie shell --seed 2018225 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))