Average Error: 58.1 → 58.1
Time: 32.8s
Precision: 64
Internal Precision: 384
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\frac{{\left((e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^*\right)}^{3} + {\left((\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right)}^{3}}{(\left({33096}^{6} \cdot 333.75\right) \cdot \left({33096}^{6} \cdot 333.75 - (\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right) + \left((\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + \left(5.5 \cdot {33096}^{8}\right))_* \cdot \left(\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + 5.5 \cdot {33096}^{8}\right)\right))_*} + \frac{77617}{2 \cdot 33096}\]

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. Using strategy rm

  3. Applied associate-+l+58.1

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

  4. Applied simplify58.1

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

  6. Applied expm1-log1p-u58.1

    \[\leadsto \left(\color{blue}{(e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^*} + (\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right) + \frac{77617}{2 \cdot 33096}\]
  7. Using strategy rm

  8. Applied flip3-+58.1

    \[\leadsto \color{blue}{\frac{{\left((e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^*\right)}^{3} + {\left((\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right)}^{3}}{(e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^* \cdot (e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^* + \left((\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_* \cdot (\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_* - (e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^* \cdot (\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right)}} + \frac{77617}{2 \cdot 33096}\]

  9. Applied simplify58.1

    \[\leadsto \frac{{\left((e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^*\right)}^{3} + {\left((\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right)}^{3}}{\color{blue}{(\left({33096}^{6} \cdot 333.75\right) \cdot \left({33096}^{6} \cdot 333.75 - (\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right) + \left((\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + \left(5.5 \cdot {33096}^{8}\right))_* \cdot (\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right))_*}} + \frac{77617}{2 \cdot 33096}\]
  10. Using strategy rm

  11. Applied fma-udef58.1

    \[\leadsto \frac{{\left((e^{\log_* (1 + 333.75 \cdot {33096}^{6})} - 1)^*\right)}^{3} + {\left((\left(77617 \cdot 77617\right) \cdot \left((11 \cdot \left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right)\right) + -2)_* + (-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right)}^{3}}{(\left({33096}^{6} \cdot 333.75\right) \cdot \left({33096}^{6} \cdot 333.75 - (\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + \left(5.5 \cdot {33096}^{8}\right))_*\right) + \left((\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + \left(5.5 \cdot {33096}^{8}\right))_* \cdot \color{blue}{\left(\left(77617 \cdot 77617\right) \cdot \left((-121 \cdot \left({33096}^{4}\right) + \left(-{33096}^{6}\right))_* + (11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2)_*\right) + 5.5 \cdot {33096}^{8}\right)}\right))_*} + \frac{77617}{2 \cdot 33096}\]

Runtime

Time bar (total: 32.8s)Debug logProfile

herbie shell --seed '#(1070131407 1246090267 3027482374 2150728003 2026520792 2347815650)' +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))))