Average Error: 0.9 → 0.9
Time: 1.4m
Precision: 64
Ground Truth: 128
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}\right)}\]
⬇
\[\sqrt{\frac{1 + \frac1{\sqrt{\left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right) \cdot {\left(\frac{\ell + \ell}{Om}\right)}^2 + 1}}}{2}}\]

Error

Bits error versus l

Bits error versus Om

Bits error versus kx

Bits error versus ky

Derivation

  1. Initial program 0.9

    \[\sqrt{\frac{1}{2} \cdot \left(1 + \frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}\right)}\]

  2. Applied simplify 0.9

    \[\leadsto \color{blue}{\sqrt{\frac{1 + \frac1{\sqrt{\left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right) \cdot {\left(\frac{\ell + \ell}{Om}\right)}^2 + 1}}}{2}}}\]
  3. Removed slow pow expressions

Runtime

Total time: 1.4m Debug log

Please include this information when filing a bug report:

herbie --seed '#(3359081009 25983739 1779362399 1820738601 703432278 2497583155)'
(FPCore (l Om kx ky)
  :name "Toniolo and Linder, Equation (3a)"
  (sqrt (* (/ 1 2) (+ 1 (/ (sqrt (+ 1 (* (sqr (/ (* 2 l) Om)) (+ (sqr (sin kx)) (sqr (sin ky)))))))))))