Average Error: 1.1 → 1.1
Time: 14.9s
Precision: 64
Internal precision: 384
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}\right)}\]
⬇
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac1{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^2 \cdot \left({\left(\sin kx\right)}^2 + {\left(\sin ky\right)}^2\right)}}\right)}\]

Error

Bits error versus l

Bits error versus Om

Bits error versus kx

Bits error versus ky

Derivation

  1. Initial program 1.1

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

Runtime

Time bar (total: 14.9s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(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)))))))))))