Average Error: 58.1 → 63.0

Time: 19.8s

Precision: 64

Internal Precision: 384

\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]

↓

\[\frac{77617}{66192} + \left(\left(1314174534371215466459037696 \cdot 333.75 + -7917111779274712207494296632228773890\right) + 5.5 \cdot 1439474789212538429291115400277262336\right)\]

Error

Derivation

Initial program 58.1
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
Applied simplify63.0
\[\leadsto \color{blue}{\frac{77617}{66192} + \left(\left(1314174534371215466459037696 \cdot 333.75 + -7917111779274712207494296632228773890\right) + 5.5 \cdot 1439474789212538429291115400277262336\right)}\]

Runtime

herbie shell --seed '#(1070991898 1055468627 4280279443 640792587 928206309 3646738750)' 
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096))))