Average Error: 0.5 → 0.5
Time: 20.8s
Precision: 64
Internal precision: 384
\[\frac{1 - 5 \cdot {v}^2}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot {v}^2\right)}\right) \cdot \left(1 - {v}^2\right)}\]
⬇
\[\frac{1 - 5 \cdot {v}^2}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot {v}^2\right)}\right)\right) \cdot \left(1 - {v}^2\right)}\]

Error

Bits error versus v

Bits error versus t

Derivation

  1. Initial program 0.5

    \[\frac{1 - 5 \cdot {v}^2}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot {v}^2\right)}\right) \cdot \left(1 - {v}^2\right)}\]
  2. Using strategy rm

  3. Applied associate-*l* 0.5

    \[\leadsto \frac{1 - 5 \cdot {v}^2}{\color{blue}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot {v}^2\right)}\right)\right)} \cdot \left(1 - {v}^2\right)}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 20.8s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (sqr v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (sqr v)))))) (- 1 (sqr v)))))