Average Error: 19.5 → 15.9
Time: 14.0s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \le 5.0807378834828 \cdot 10^{-309}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{A}{V}} \cdot \sqrt{\frac{1}{\ell}}\right) \cdot c0\\ \end{array}\]

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 2 regimes

  2. if l < 5.0807378834828e-309

    1. Initial program 20.0

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

    2. Initial simplification19.6

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

    4. Applied *-commutative19.6

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

    if 5.0807378834828e-309 < l

    1. Initial program 18.9

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

    2. Initial simplification19.1

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

    4. Applied div-inv19.1

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

    5. Applied sqrt-prod12.0

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{A}{V}} \cdot \sqrt{\frac{1}{\ell}}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification15.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le 5.0807378834828 \cdot 10^{-309}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{A}{V}} \cdot \sqrt{\frac{1}{\ell}}\right) \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 14.0s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes19.415.911.18.242.6%
herbie shell --seed 2018339 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))