From Warwick Tucker's Validated Numerics

Average Error: 58.1 → 63.0

Time: 13.9s

Precision: 64

Math

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

↓

\[\left(\left(\left(5.5 \cdot 1439474789212538429291115400277262336 + -7917111779274712207494296620179976512\right) + -12048797378\right) + {\left({\left(e^{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)} \cdot \sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}} \cdot \sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}\right) + \frac{77617}{66192}\]

C

double f() {
        double r990082 = 333.75;
        double r990083 = 33096.0;
        double r990084 = 6.0;
        double r990085 = pow(r990083, r990084);
        double r990086 = r990082 * r990085;
        double r990087 = 77617.0;
        double r990088 = r990087 * r990087;
        double r990089 = 11.0;
        double r990090 = r990089 * r990088;
        double r990091 = r990083 * r990083;
        double r990092 = r990090 * r990091;
        double r990093 = -r990085;
        double r990094 = r990092 + r990093;
        double r990095 = -121.0;
        double r990096 = 4.0;
        double r990097 = pow(r990083, r990096);
        double r990098 = r990095 * r990097;
        double r990099 = r990094 + r990098;
        double r990100 = -2.0;
        double r990101 = r990099 + r990100;
        double r990102 = r990088 * r990101;
        double r990103 = r990086 + r990102;
        double r990104 = 5.5;
        double r990105 = 8.0;
        double r990106 = pow(r990083, r990105);
        double r990107 = r990104 * r990106;
        double r990108 = r990103 + r990107;
        double r990109 = 2.0;
        double r990110 = r990109 * r990083;
        double r990111 = r990087 / r990110;
        double r990112 = r990108 + r990111;
        return r990112;
}

↓

double f() {
        double r990113 = 5.5;
        double r990114 = 1.4394747892125385e+36;
        double r990115 = r990113 * r990114;
        double r990116 = -7.917111779274712e+36;
        double r990117 = r990115 + r990116;
        double r990118 = -12048797378.0;
        double r990119 = r990117 + r990118;
        double r990120 = 1.3141745343712155e+27;
        double r990121 = 333.75;
        double r990122 = r990120 * r990121;
        double r990123 = log(r990122);
        double r990124 = cbrt(r990123);
        double r990125 = r990124 * r990124;
        double r990126 = exp(r990125);
        double r990127 = cbrt(r990124);
        double r990128 = r990127 * r990127;
        double r990129 = pow(r990126, r990128);
        double r990130 = pow(r990129, r990127);
        double r990131 = r990119 + r990130;
        double r990132 = 1.1726039400531787;
        double r990133 = r990131 + r990132;
        return r990133;
}

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. Simplified 58.1

   \[\leadsto \left(333.75 \cdot {33096}^{6} + \color{blue}{\left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)}\right) + \frac{77617}{2 \cdot 33096}\]
5. Using strategy rm

6. Applied pow-to-exp 58.1

   \[\leadsto \left(333.75 \cdot \color{blue}{e^{\log 33096 \cdot 6}} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]

7. Applied add-exp-log 58.1

   \[\leadsto \left(\color{blue}{e^{\log 333.75}} \cdot e^{\log 33096 \cdot 6} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]

8. Applied prod-exp 58.1

   \[\leadsto \left(\color{blue}{e^{\log 333.75 + \log 33096 \cdot 6}} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]

9. Simplified 58.1

   \[\leadsto \left(e^{\color{blue}{\log \left(1314174534371215466459037696 \cdot 333.75\right)}} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]
10. Using strategy rm

11. Applied add-cube-cbrt 58.1

    \[\leadsto \left(e^{\color{blue}{\left(\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)} \cdot \sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}\right) \cdot \sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]

12. Applied exp-prod 58.1

    \[\leadsto \left(\color{blue}{{\left(e^{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)} \cdot \sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}^{\left(\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}\right)}} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]
13. Using strategy rm

14. Applied add-cube-cbrt 58.1

    \[\leadsto \left({\left(e^{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)} \cdot \sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}^{\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}} \cdot \sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]

15. Applied pow-unpow 58.1

    \[\leadsto \left(\color{blue}{{\left({\left(e^{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)} \cdot \sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}} \cdot \sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}} + \left(\left(5.5 \cdot 1439474789212538429291115400277262336 + \left(-7917110904691559438276885483785904448 + -874583152769217411136394072064\right)\right) + -12048797378\right)\right) + \frac{77617}{2 \cdot 33096}\]

16. Final simplification 63.0

    \[\leadsto \left(\left(\left(5.5 \cdot 1439474789212538429291115400277262336 + -7917111779274712207494296620179976512\right) + -12048797378\right) + {\left({\left(e^{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)} \cdot \sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}} \cdot \sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(1314174534371215466459037696 \cdot 333.75\right)}}\right)}\right) + \frac{77617}{66192}\]

Reproduce

herbie shell --seed 2019128 
(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))))