From Warwick Tucker's Validated Numerics

Average Error: 58.1 → 58.1

Time: 21.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f() {
        double r67101 = 333.75;
        double r67102 = 33096.0;
        double r67103 = 6.0;
        double r67104 = pow(r67102, r67103);
        double r67105 = r67101 * r67104;
        double r67106 = 77617.0;
        double r67107 = r67106 * r67106;
        double r67108 = 11.0;
        double r67109 = r67108 * r67107;
        double r67110 = r67102 * r67102;
        double r67111 = r67109 * r67110;
        double r67112 = -r67104;
        double r67113 = r67111 + r67112;
        double r67114 = -121.0;
        double r67115 = 4.0;
        double r67116 = pow(r67102, r67115);
        double r67117 = r67114 * r67116;
        double r67118 = r67113 + r67117;
        double r67119 = -2.0;
        double r67120 = r67118 + r67119;
        double r67121 = r67107 * r67120;
        double r67122 = r67105 + r67121;
        double r67123 = 5.5;
        double r67124 = 8.0;
        double r67125 = pow(r67102, r67124);
        double r67126 = r67123 * r67125;
        double r67127 = r67122 + r67126;
        double r67128 = 2.0;
        double r67129 = r67128 * r67102;
        double r67130 = r67106 / r67129;
        double r67131 = r67127 + r67130;
        return r67131;
}

↓

double f() {
        double r67132 = 5.5;
        double r67133 = 33096.0;
        double r67134 = 8.0;
        double r67135 = pow(r67133, r67134);
        double r67136 = r67132 * r67135;
        double r67137 = 3.0;
        double r67138 = pow(r67136, r67137);
        double r67139 = 77617.0;
        double r67140 = r67139 * r67139;
        double r67141 = -121.0;
        double r67142 = 4.0;
        double r67143 = pow(r67133, r67142);
        double r67144 = r67141 * r67143;
        double r67145 = 11.0;
        double r67146 = r67145 * r67140;
        double r67147 = r67133 * r67133;
        double r67148 = r67146 * r67147;
        double r67149 = 6.0;
        double r67150 = pow(r67133, r67149);
        double r67151 = r67148 - r67150;
        double r67152 = r67144 + r67151;
        double r67153 = -2.0;
        double r67154 = r67152 + r67153;
        double r67155 = r67140 * r67154;
        double r67156 = 333.75;
        double r67157 = r67156 * r67150;
        double r67158 = r67155 + r67157;
        double r67159 = 2.0;
        double r67160 = pow(r67158, r67159);
        double r67161 = r67160 * r67158;
        double r67162 = r67138 + r67161;
        double r67163 = r67158 * r67158;
        double r67164 = cbrt(r67133);
        double r67165 = r67164 * r67164;
        double r67166 = pow(r67165, r67134);
        double r67167 = r67132 * r67166;
        double r67168 = sqrt(r67133);
        double r67169 = cbrt(r67168);
        double r67170 = pow(r67169, r67134);
        double r67171 = r67170 * r67170;
        double r67172 = r67167 * r67171;
        double r67173 = r67172 - r67158;
        double r67174 = r67136 * r67173;
        double r67175 = r67163 + r67174;
        double r67176 = r67162 / r67175;
        double r67177 = 2.0;
        double r67178 = r67177 * r67133;
        double r67179 = r67139 / r67178;
        double r67180 = r67176 + r67179;
        return r67180;
}

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

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

5. Simplified 58.1

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

7. Applied add-cube-cbrt 58.1

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

8. Applied unpow-prod-down 58.1

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

9. Simplified 58.1

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

10. Simplified 58.1

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

12. Applied add-cube-cbrt 58.1

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

13. Applied unpow-prod-down 58.1

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

14. Applied associate-*r* 58.1

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

16. Applied add-sqr-sqrt 58.1

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

17. Applied cbrt-prod 58.1

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

18. Applied unpow-prod-down 58.1

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

19. Final simplification 58.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 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))))