Average Error: 58.1 → 58.1
Time: 23.5s
Precision: 64
Internal precision: 640
\[\left(\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
⬇
\[\frac{{e}^{\left(\log \left({\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2\right)\right)}}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}} + \frac{77617}{2 \cdot 33096}\]

Error

Derivation

  1. Initial program 58.1

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

  3. Applied flip-+ 58.1

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

  5. Applied add-exp-log 58.1

    \[\leadsto \frac{\color{blue}{e^{\log \left({\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2\right)}}}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}} + \frac{77617}{2 \cdot 33096}\]
  6. Using strategy rm

  7. Applied pow1 58.1

    \[\leadsto \frac{e^{\log \color{blue}{\left({\left({\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2\right)}^{1}\right)}}}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}} + \frac{77617}{2 \cdot 33096}\]

  8. Applied log-pow 58.1

    \[\leadsto \frac{e^{\color{blue}{1 \cdot \log \left({\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2\right)}}}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}} + \frac{77617}{2 \cdot 33096}\]

  9. Applied exp-prod 58.1

    \[\leadsto \frac{\color{blue}{{\left(e^{1}\right)}^{\left(\log \left({\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2\right)\right)}}}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}} + \frac{77617}{2 \cdot 33096}\]

  10. Applied simplify 58.1

    \[\leadsto \frac{{\color{blue}{e}}^{\left(\log \left({\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right)}^2 - {\left(5.5 \cdot {33096}^{8}\right)}^2\right)\right)}}{\left(333.75 \cdot {33096}^{6} + {77617}^2 \cdot \left(\left(\left(\left(11 \cdot {77617}^2\right) \cdot {33096}^2 + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) - 5.5 \cdot {33096}^{8}} + \frac{77617}{2 \cdot 33096}\]
  11. Removed slow pow expressions

Runtime

Time bar (total: 23.5s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 333.75 (pow 33096 6)) (* (sqr 77617) (+ (+ (+ (* (* 11 (sqr 77617)) (sqr 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096))))