Average Error: 19.3 → 12.4
Time: 55.6s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \cdot V \le -7.014771159252155 \cdot 10^{+191}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;\ell \cdot V \le -1.246902747429659 \cdot 10^{-193}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right)\\ \mathbf{elif}\;\ell \cdot V \le 3.63229353969324 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \end{array}\]

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) < -7.014771159252155e+191 or -1.246902747429659e-193 < (* V l) < 3.63229353969324e-310

    1. Initial program 38.6

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

    3. Applied associate-/r*26.2

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

    if -7.014771159252155e+191 < (* V l) < -1.246902747429659e-193

    1. Initial program 7.2

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

    3. Applied add-sqr-sqrt7.2

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

    4. Applied sqrt-prod7.5

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

    if 3.63229353969324e-310 < (* V l)

    1. Initial program 14.7

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

    3. Applied div-inv14.8

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

    4. Applied sqrt-prod6.8

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

  4. Final simplification12.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \le -7.014771159252155 \cdot 10^{+191}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{elif}\;\ell \cdot V \le -1.246902747429659 \cdot 10^{-193}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\sqrt{\frac{A}{\ell \cdot V}}} \cdot \sqrt{\sqrt{\frac{A}{\ell \cdot V}}}\right)\\ \mathbf{elif}\;\ell \cdot V \le 3.63229353969324 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \end{array}\]

Runtime

Time bar (total: 55.6s)Debug logProfile

herbie shell --seed 2018214 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))