Average Error: 18.6 → 12.6
Time: 14.4s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.506696411579775 \cdot 10^{+110}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.2080400555973046 \cdot 10^{-111}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 1.497502947285194 \cdot 10^{-309}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (* V l) < -7.506696411579775e+110 or -1.2080400555973046e-111 < (* V l) < 1.497502947285194e-309

    1. Initial program 30.9

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

    3. Applied associate-/r*24.3

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

    if -7.506696411579775e+110 < (* V l) < -1.2080400555973046e-111

    1. Initial program 3.9

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

    3. Applied add-sqr-sqrt4.2

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

    4. Applied associate-*r*4.1

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

    6. Applied clear-num4.3

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

    if 1.497502947285194e-309 < (* V l)

    1. Initial program 14.2

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

    3. Applied sqrt-div6.2

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

  4. Final simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.506696411579775 \cdot 10^{+110}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.2080400555973046 \cdot 10^{-111}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 1.497502947285194 \cdot 10^{-309}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 14.4s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes18.912.610.48.574.8%
herbie shell --seed 2018295 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))