Average Error: 58.1 → 58.1
Time: 10.9s
Precision: 64
Internal Precision: 576
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[(\left(\left(\left(77617 \cdot 77617\right) \cdot \left(33096 \cdot 33096\right)\right) \cdot 11 - \left({33096}^{6} - (-121 \cdot \left({33096}^{4}\right) + -2)_*\right)\right) \cdot \left(77617 \cdot 77617\right) + \left((\left({33096}^{6}\right) \cdot 333.75 + \left((\left({33096}^{8}\right) \cdot 5.5 + \left(\frac{\frac{77617}{2}}{33096}\right))_*\right))_*\right))_*\]

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. Initial simplification58.1

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

  3. Final simplification58.1

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

Runtime

Time bar (total: 10.9s)Debug logProfile

herbie shell --seed 2018216 +o rules:numerics
(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))))