Average Error: 58.1 → 56.8
Time: 43.2s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\sqrt[3]{\left(\left(\left(333.75 \cdot {33096}^{6} + {33096}^{8} \cdot 5.5\right) + \left(\left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2\right) - \left({33096}^{6} - {33096}^{4} \cdot -121\right)\right) \cdot \left(77617 \cdot 77617\right)\right)\right) + \frac{77617}{33096 \cdot 2}} \cdot \left(\sqrt[3]{\left(\left(\left(333.75 \cdot {33096}^{6} + {33096}^{8} \cdot 5.5\right) + \left(\left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2\right) - \left({33096}^{6} - {33096}^{4} \cdot -121\right)\right) \cdot \left(77617 \cdot 77617\right)\right)\right) + \frac{77617}{33096 \cdot 2}} \cdot \sqrt[3]{\left(\left(\left(333.75 \cdot {33096}^{6} + {33096}^{8} \cdot 5.5\right) + \left(\left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2\right) - \left({33096}^{6} - {33096}^{4} \cdot -121\right)\right) \cdot \left(77617 \cdot 77617\right)\right)\right) + \frac{77617}{33096 \cdot 2}}\right)\]
\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}
↓
\sqrt[3]{\left(\left(\left(333.75 \cdot {33096}^{6} + {33096}^{8} \cdot 5.5\right) + \left(\left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2\right) - \left({33096}^{6} - {33096}^{4} \cdot -121\right)\right) \cdot \left(77617 \cdot 77617\right)\right)\right) + \frac{77617}{33096 \cdot 2}} \cdot \left(\sqrt[3]{\left(\left(\left(333.75 \cdot {33096}^{6} + {33096}^{8} \cdot 5.5\right) + \left(\left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2\right) - \left({33096}^{6} - {33096}^{4} \cdot -121\right)\right) \cdot \left(77617 \cdot 77617\right)\right)\right) + \frac{77617}{33096 \cdot 2}} \cdot \sqrt[3]{\left(\left(\left(333.75 \cdot {33096}^{6} + {33096}^{8} \cdot 5.5\right) + \left(\left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) + -2\right) - \left({33096}^{6} - {33096}^{4} \cdot -121\right)\right) \cdot \left(77617 \cdot 77617\right)\right)\right) + \frac{77617}{33096 \cdot 2}}\right)
double f() {
        double r4746789 = 333.75;
        double r4746790 = 33096.0;
        double r4746791 = 6.0;
        double r4746792 = pow(r4746790, r4746791);
        double r4746793 = r4746789 * r4746792;
        double r4746794 = 77617.0;
        double r4746795 = r4746794 * r4746794;
        double r4746796 = 11.0;
        double r4746797 = r4746796 * r4746795;
        double r4746798 = r4746790 * r4746790;
        double r4746799 = r4746797 * r4746798;
        double r4746800 = -r4746792;
        double r4746801 = r4746799 + r4746800;
        double r4746802 = -121.0;
        double r4746803 = 4.0;
        double r4746804 = pow(r4746790, r4746803);
        double r4746805 = r4746802 * r4746804;
        double r4746806 = r4746801 + r4746805;
        double r4746807 = -2.0;
        double r4746808 = r4746806 + r4746807;
        double r4746809 = r4746795 * r4746808;
        double r4746810 = r4746793 + r4746809;
        double r4746811 = 5.5;
        double r4746812 = 8.0;
        double r4746813 = pow(r4746790, r4746812);
        double r4746814 = r4746811 * r4746813;
        double r4746815 = r4746810 + r4746814;
        double r4746816 = 2.0;
        double r4746817 = r4746816 * r4746790;
        double r4746818 = r4746794 / r4746817;
        double r4746819 = r4746815 + r4746818;
        return r4746819;
}
↓
double f() {
        double r4746820 = 333.75;
        double r4746821 = 33096.0;
        double r4746822 = 6.0;
        double r4746823 = pow(r4746821, r4746822);
        double r4746824 = r4746820 * r4746823;
        double r4746825 = 8.0;
        double r4746826 = pow(r4746821, r4746825);
        double r4746827 = 5.5;
        double r4746828 = r4746826 * r4746827;
        double r4746829 = r4746824 + r4746828;
        double r4746830 = 11.0;
        double r4746831 = 77617.0;
        double r4746832 = r4746821 * r4746831;
        double r4746833 = r4746832 * r4746832;
        double r4746834 = r4746830 * r4746833;
        double r4746835 = -2.0;
        double r4746836 = r4746834 + r4746835;
        double r4746837 = 4.0;
        double r4746838 = pow(r4746821, r4746837);
        double r4746839 = -121.0;
        double r4746840 = r4746838 * r4746839;
        double r4746841 = r4746823 - r4746840;
        double r4746842 = r4746836 - r4746841;
        double r4746843 = r4746831 * r4746831;
        double r4746844 = r4746842 * r4746843;
        double r4746845 = r4746829 + r4746844;
        double r4746846 = /* ERROR: no posit support in C */;
        double r4746847 = /* ERROR: no posit support in C */;
        double r4746848 = 2.0;
        double r4746849 = r4746821 * r4746848;
        double r4746850 = r4746831 / r4746849;
        double r4746851 = r4746847 + r4746850;
        double r4746852 = cbrt(r4746851);
        double r4746853 = r4746852 * r4746852;
        double r4746854 = r4746852 * r4746853;
        return r4746854;
}

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 insert-posit1656.8

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

  4. Simplified56.8

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

  6. Applied add-cube-cbrt56.8

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

  7. Final simplification56.8

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

Reproduce

herbie shell --seed 2019168 
(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))))