Average Error: 18.9 → 11.3
Time: 41.2s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \le -1.4465936640347471 \cdot 10^{+295}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{if}\;\ell \cdot V \le -1.7850903931179766 \cdot 10^{-56}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right) \cdot c0\\ \mathbf{if}\;\ell \cdot V \le 1.2845706791872 \cdot 10^{-322} \lor \neg \left(\ell \cdot V \le 1.7811482673865394 \cdot 10^{+308}\right):\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]

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 3 regimes

  2. if (* V l) < -1.4465936640347471e+295 or -1.7850903931179766e-56 < (* V l) < 1.2845706791872e-322 or 1.7811482673865394e+308 < (* V l)

    1. Initial program 34.7

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

    3. Applied associate-/r*24.0

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

    if -1.4465936640347471e+295 < (* V l) < -1.7850903931179766e-56

    1. Initial program 7.6

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

    3. Applied add-sqr-sqrt7.6

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

    4. Applied sqrt-prod7.8

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

    if 1.2845706791872e-322 < (* V l) < 1.7811482673865394e+308

    1. Initial program 10.4

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

    3. Applied sqrt-div0.7

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

  4. Applied simplify11.3

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\ell \cdot V \le -1.4465936640347471 \cdot 10^{+295}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{if}\;\ell \cdot V \le -1.7850903931179766 \cdot 10^{-56}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right) \cdot c0\\ \mathbf{if}\;\ell \cdot V \le 1.2845706791872 \cdot 10^{-322} \lor \neg \left(\ell \cdot V \le 1.7811482673865394 \cdot 10^{+308}\right):\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}}\]

Runtime

Time bar (total: 41.2s)Debug logProfile

herbie shell --seed 2020178 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))