Error

Derivation

1. Split input into 3 regimes

2. if (/ A l) < 3.2138083397342488e-252

   1. Initial program 19.4

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

   if 3.2138083397342488e-252 < (/ A l) < 4.533790555896115e+298

   1. Initial program 16.2

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

   3. Applied associate-/r*15.3

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

   5. Applied div-inv15.4

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}}\]
   6. Using strategy rm

   7. Applied associate-*l/9.0

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

   8. Applied sqrt-div0.4

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

   9. Applied simplify0.4

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

   if 4.533790555896115e+298 < (/ A l)

   1. Initial program 34.6

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

   3. Applied associate-/r*34.6

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

   5. Applied sqrt-div38.0

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

   6. Applied associate-*r/38.4

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

Runtime

Time bar (total: 35.3s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))