From Warwick Tucker's Validated Numerics

Average Error: 58.1 → 58.1

Time: 14.0s

Precision: 64

Math

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

↓

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

C

double f() {
        double r38929 = 333.75;
        double r38930 = 33096.0;
        double r38931 = 6.0;
        double r38932 = pow(r38930, r38931);
        double r38933 = r38929 * r38932;
        double r38934 = 77617.0;
        double r38935 = r38934 * r38934;
        double r38936 = 11.0;
        double r38937 = r38936 * r38935;
        double r38938 = r38930 * r38930;
        double r38939 = r38937 * r38938;
        double r38940 = -r38932;
        double r38941 = r38939 + r38940;
        double r38942 = -121.0;
        double r38943 = 4.0;
        double r38944 = pow(r38930, r38943);
        double r38945 = r38942 * r38944;
        double r38946 = r38941 + r38945;
        double r38947 = -2.0;
        double r38948 = r38946 + r38947;
        double r38949 = r38935 * r38948;
        double r38950 = r38933 + r38949;
        double r38951 = 5.5;
        double r38952 = 8.0;
        double r38953 = pow(r38930, r38952);
        double r38954 = r38951 * r38953;
        double r38955 = r38950 + r38954;
        double r38956 = 2.0;
        double r38957 = r38956 * r38930;
        double r38958 = r38934 / r38957;
        double r38959 = r38955 + r38958;
        return r38959;
}

↓

double f() {
        double r38960 = 77617.0;
        double r38961 = 2.0;
        double r38962 = 33096.0;
        double r38963 = r38961 * r38962;
        double r38964 = r38960 / r38963;
        double r38965 = 8.0;
        double r38966 = pow(r38962, r38965);
        double r38967 = 5.5;
        double r38968 = r38966 * r38967;
        double r38969 = 3.0;
        double r38970 = pow(r38968, r38969);
        double r38971 = -121.0;
        double r38972 = 4.0;
        double r38973 = pow(r38962, r38972);
        double r38974 = r38971 * r38973;
        double r38975 = -2.0;
        double r38976 = r38962 * r38962;
        double r38977 = r38960 * r38960;
        double r38978 = r38976 * r38977;
        double r38979 = 11.0;
        double r38980 = r38978 * r38979;
        double r38981 = 6.0;
        double r38982 = pow(r38962, r38981);
        double r38983 = r38980 - r38982;
        double r38984 = r38975 + r38983;
        double r38985 = r38974 + r38984;
        double r38986 = r38985 * r38977;
        double r38987 = 333.75;
        double r38988 = r38982 * r38987;
        double r38989 = r38986 + r38988;
        double r38990 = r38989 * r38989;
        double r38991 = r38989 * r38990;
        double r38992 = r38970 + r38991;
        double r38993 = r38968 - r38988;
        double r38994 = r38993 - r38986;
        double r38995 = r38967 * r38994;
        double r38996 = r38966 * r38995;
        double r38997 = r38996 + r38990;
        double r38998 = r38992 / r38997;
        double r38999 = r38964 + r38998;
        return r38999;
}

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 flip3-+ 58.1

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

4. Simplified 58.1

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

5. Simplified 58.1

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

7. Applied add-cbrt-cube 58.2

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

8. Applied rem-cube-cbrt 58.1

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

9. Final simplification 58.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 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))))