From Warwick Tucker's Validated Numerics

Average Error: 58.1 → 58.1

Time: 8.8s

Precision: binary64

Math

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

↓

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

FPCore

(FPCore ()
 :precision binary64
 (+
  (+
   (+
    (* 333.75 (pow 33096.0 6.0))
    (*
     (* 77617.0 77617.0)
     (+
      (+
       (+
        (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0))
        (- (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))))

↓

(FPCore ()
 :precision binary64
 (+
  (/
   (+
    (*
     (+
      (* 333.75 (pow 33096.0 6.0))
      (*
       (* 77617.0 77617.0)
       (+
        (+
         (-
          (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
          (pow 33096.0 6.0))
         (* -121.0 (pow 33096.0 4.0)))
        -2.0)))
     (pow
      (+
       (* 333.75 (pow 33096.0 6.0))
       (*
        (* 77617.0 77617.0)
        (+
         (+
          (-
           (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
           (pow 33096.0 6.0))
          (* -121.0 (pow 33096.0 4.0)))
         -2.0)))
      2.0))
    (pow (* 5.5 (pow 33096.0 8.0)) 3.0))
   (+
    (*
     (+
      (* 333.75 (pow 33096.0 6.0))
      (*
       (* 77617.0 77617.0)
       (+
        (+
         (-
          (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
          (pow 33096.0 6.0))
         (* -121.0 (pow 33096.0 4.0)))
        -2.0)))
     (+
      (* 333.75 (pow 33096.0 6.0))
      (*
       (* 77617.0 77617.0)
       (+
        -2.0
        (+
         (* -121.0 (pow 33096.0 4.0))
         (*
          (cbrt
           (-
            (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
            (pow 33096.0 6.0)))
          (*
           (cbrt
            (-
             (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
             (pow 33096.0 6.0)))
           (cbrt
            (-
             (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
             (pow 33096.0 6.0))))))))))
    (*
     5.5
     (*
      (pow 33096.0 8.0)
      (-
       (* 5.5 (pow 33096.0 8.0))
       (+
        (* 333.75 (pow 33096.0 6.0))
        (*
         (* 77617.0 77617.0)
         (+
          -2.0
          (+
           (* -121.0 (pow 33096.0 4.0))
           (*
            (cbrt
             (-
              (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
              (pow 33096.0 6.0)))
            (*
             (cbrt
              (-
               (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
               (pow 33096.0 6.0)))
             (cbrt
              (-
               (* (* (* 77617.0 77617.0) 11.0) (* 33096.0 33096.0))
               (pow 33096.0 6.0))))))))))))))
  (/ 77617.0 (* 33096.0 2.0))))

C

double code() {
	return ((double) (((double) (((double) (((double) (333.75 * ((double) pow(33096.0, 6.0)))) + ((double) (((double) (77617.0 * 77617.0)) * ((double) (((double) (((double) (((double) (((double) (11.0 * ((double) (77617.0 * 77617.0)))) * ((double) (33096.0 * 33096.0)))) + ((double) -(((double) pow(33096.0, 6.0)))))) + ((double) (-121.0 * ((double) pow(33096.0, 4.0)))))) + -2.0)))))) + ((double) (5.5 * ((double) pow(33096.0, 8.0)))))) + (77617.0 / ((double) (2.0 * 33096.0)))));
}

↓

double code() {
	return ((double) ((((double) (((double) (((double) (((double) (333.75 * ((double) pow(33096.0, 6.0)))) + ((double) (((double) (77617.0 * 77617.0)) * ((double) (((double) (((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))) + ((double) (-121.0 * ((double) pow(33096.0, 4.0)))))) + -2.0)))))) * ((double) pow(((double) (((double) (333.75 * ((double) pow(33096.0, 6.0)))) + ((double) (((double) (77617.0 * 77617.0)) * ((double) (((double) (((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))) + ((double) (-121.0 * ((double) pow(33096.0, 4.0)))))) + -2.0)))))), 2.0)))) + ((double) pow(((double) (5.5 * ((double) pow(33096.0, 8.0)))), 3.0)))) / ((double) (((double) (((double) (((double) (333.75 * ((double) pow(33096.0, 6.0)))) + ((double) (((double) (77617.0 * 77617.0)) * ((double) (((double) (((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))) + ((double) (-121.0 * ((double) pow(33096.0, 4.0)))))) + -2.0)))))) * ((double) (((double) (333.75 * ((double) pow(33096.0, 6.0)))) + ((double) (((double) (77617.0 * 77617.0)) * ((double) (-2.0 + ((double) (((double) (-121.0 * ((double) pow(33096.0, 4.0)))) + ((double) (((double) cbrt(((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))))) * ((double) (((double) cbrt(((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))))) * ((double) cbrt(((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))))))))))))))))))) + ((double) (5.5 * ((double) (((double) pow(33096.0, 8.0)) * ((double) (((double) (5.5 * ((double) pow(33096.0, 8.0)))) - ((double) (((double) (333.75 * ((double) pow(33096.0, 6.0)))) + ((double) (((double) (77617.0 * 77617.0)) * ((double) (-2.0 + ((double) (((double) (-121.0 * ((double) pow(33096.0, 4.0)))) + ((double) (((double) cbrt(((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))))) * ((double) (((double) cbrt(((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0)))))) * ((double) cbrt(((double) (((double) (((double) (((double) (77617.0 * 77617.0)) * 11.0)) * ((double) (33096.0 * 33096.0)))) - ((double) pow(33096.0, 6.0))))))))))))))))))))))))))) + (77617.0 / ((double) (33096.0 * 2.0)))));
}

Derivation

1. Initial program Error: 58.1 bits

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

2. Simplified Error: 58.1 bits

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

4. Applied flip3-+ Error: 58.1 bits

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

5. Simplified Error: 58.1 bits

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

7. Applied add-cube-cbrt Error: 58.1 bits

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

8. Applied unpow-prod-down Error: 58.1 bits

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

9. Simplified Error: 58.1 bits

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

10. Simplified Error: 58.1 bits

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

12. Applied add-cube-cbrt Error: 58.1 bits

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

14. Applied add-cube-cbrt Error: 58.1 bits

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

15. Final simplification Error: 58.1 bits

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

Reproduce

herbie shell --seed 2020205 
(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)) (- (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))))