Average Error: 58.1 → 63.6
Time: 19.4s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\frac{77617}{66192} + \frac{{\left(e^{\sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)} \cdot \sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)}\right)}}{\left(-7917111779274712207494296632228773890 + \left(\left(1314174534371215466459037696 \cdot 333.75\right)\right)\right) - 1439474789212538429291115400277262336 \cdot 5.5}\]
\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}{66192} + \frac{{\left(e^{\sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)} \cdot \sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)}\right)}}{\left(-7917111779274712207494296632228773890 + \left(\left(1314174534371215466459037696 \cdot 333.75\right)\right)\right) - 1439474789212538429291115400277262336 \cdot 5.5}
double f() {
        double r1073773 = 333.75;
        double r1073774 = 33096.0;
        double r1073775 = 6.0;
        double r1073776 = pow(r1073774, r1073775);
        double r1073777 = r1073773 * r1073776;
        double r1073778 = 77617.0;
        double r1073779 = r1073778 * r1073778;
        double r1073780 = 11.0;
        double r1073781 = r1073780 * r1073779;
        double r1073782 = r1073774 * r1073774;
        double r1073783 = r1073781 * r1073782;
        double r1073784 = -r1073776;
        double r1073785 = r1073783 + r1073784;
        double r1073786 = -121.0;
        double r1073787 = 4.0;
        double r1073788 = pow(r1073774, r1073787);
        double r1073789 = r1073786 * r1073788;
        double r1073790 = r1073785 + r1073789;
        double r1073791 = -2.0;
        double r1073792 = r1073790 + r1073791;
        double r1073793 = r1073779 * r1073792;
        double r1073794 = r1073777 + r1073793;
        double r1073795 = 5.5;
        double r1073796 = 8.0;
        double r1073797 = pow(r1073774, r1073796);
        double r1073798 = r1073795 * r1073797;
        double r1073799 = r1073794 + r1073798;
        double r1073800 = 2.0;
        double r1073801 = r1073800 * r1073774;
        double r1073802 = r1073778 / r1073801;
        double r1073803 = r1073799 + r1073802;
        return r1073803;
}
↓
double f() {
        double r1073804 = 1.1726039400531787;
        double r1073805 = -7.917111779274712e+36;
        double r1073806 = 1.3141745343712155e+27;
        double r1073807 = 333.75;
        double r1073808 = r1073806 * r1073807;
        double r1073809 = r1073805 + r1073808;
        double r1073810 = r1073809 * r1073809;
        double r1073811 = 1.4394747892125385e+36;
        double r1073812 = 5.5;
        double r1073813 = r1073811 * r1073812;
        double r1073814 = r1073813 * r1073813;
        double r1073815 = r1073810 - r1073814;
        double r1073816 = log(r1073815);
        double r1073817 = cbrt(r1073816);
        double r1073818 = r1073817 * r1073817;
        double r1073819 = exp(r1073818);
        double r1073820 = pow(r1073819, r1073817);
        double r1073821 = /* ERROR: no posit support in C */;
        double r1073822 = /* ERROR: no posit support in C */;
        double r1073823 = r1073805 + r1073822;
        double r1073824 = r1073823 - r1073813;
        double r1073825 = r1073820 / r1073824;
        double r1073826 = r1073804 + r1073825;
        return r1073826;
}

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 flip-+58.1

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

  5. Applied add-exp-log58.1

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

  7. Applied insert-posit1658.1

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

  9. Applied add-cube-cbrt58.1

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

  10. Applied exp-prod58.1

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

  11. Final simplification63.6

    \[\leadsto \frac{77617}{66192} + \frac{{\left(e^{\sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)} \cdot \sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(\left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) \cdot \left(-7917111779274712207494296632228773890 + 1314174534371215466459037696 \cdot 333.75\right) - \left(1439474789212538429291115400277262336 \cdot 5.5\right) \cdot \left(1439474789212538429291115400277262336 \cdot 5.5\right)\right)}\right)}}{\left(-7917111779274712207494296632228773890 + \left(\left(1314174534371215466459037696 \cdot 333.75\right)\right)\right) - 1439474789212538429291115400277262336 \cdot 5.5}\]

Reproduce

herbie shell --seed 2019154 
(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))))