Average Error: 58.1 → 58.1
Time: 2.9s
Precision: binary64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[333.75 \cdot {33096}^{6} + \left(77617 \cdot \left(\left(33096 \cdot \left(33096 \cdot 11\right)\right) \cdot {77617}^{3} + 77617 \cdot \left(-121 \cdot {33096}^{4} + \left(-2 - {33096}^{6}\right)\right)\right) + \left(5.5 \cdot {33096}^{8} + \frac{77617}{33096 \cdot 2}\right)\right)\]

Error

Derivation

  1. Initial program 58.1

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

  2. Simplified58.1

    \[\leadsto \color{blue}{333.75 \cdot {33096}^{6} + \left(77617 \cdot \left(\left(33096 \cdot \left(33096 \cdot 11\right)\right) \cdot {77617}^{3} + 77617 \cdot \left(-121 \cdot {33096}^{4} + \left(-2 - {33096}^{6}\right)\right)\right) + \left(5.5 \cdot {33096}^{8} + \frac{77617}{33096 \cdot 2}\right)\right)}\]

  3. Final simplification58.1

    \[\leadsto 333.75 \cdot {33096}^{6} + \left(77617 \cdot \left(\left(33096 \cdot \left(33096 \cdot 11\right)\right) \cdot {77617}^{3} + 77617 \cdot \left(-121 \cdot {33096}^{4} + \left(-2 - {33096}^{6}\right)\right)\right) + \left(5.5 \cdot {33096}^{8} + \frac{77617}{33096 \cdot 2}\right)\right)\]

Reproduce

herbie shell --seed 2020184 
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (neg (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0))))