Average Error: 58.1 → 63.6
Time: 23.8s
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 r3104947 = 333.75;
        double r3104948 = 33096.0;
        double r3104949 = 6.0;
        double r3104950 = pow(r3104948, r3104949);
        double r3104951 = r3104947 * r3104950;
        double r3104952 = 77617.0;
        double r3104953 = r3104952 * r3104952;
        double r3104954 = 11.0;
        double r3104955 = r3104954 * r3104953;
        double r3104956 = r3104948 * r3104948;
        double r3104957 = r3104955 * r3104956;
        double r3104958 = -r3104950;
        double r3104959 = r3104957 + r3104958;
        double r3104960 = -121.0;
        double r3104961 = 4.0;
        double r3104962 = pow(r3104948, r3104961);
        double r3104963 = r3104960 * r3104962;
        double r3104964 = r3104959 + r3104963;
        double r3104965 = -2.0;
        double r3104966 = r3104964 + r3104965;
        double r3104967 = r3104953 * r3104966;
        double r3104968 = r3104951 + r3104967;
        double r3104969 = 5.5;
        double r3104970 = 8.0;
        double r3104971 = pow(r3104948, r3104970);
        double r3104972 = r3104969 * r3104971;
        double r3104973 = r3104968 + r3104972;
        double r3104974 = 2.0;
        double r3104975 = r3104974 * r3104948;
        double r3104976 = r3104952 / r3104975;
        double r3104977 = r3104973 + r3104976;
        return r3104977;
}
↓
double f() {
        double r3104978 = 1.1726039400531787;
        double r3104979 = -7.917111779274712e+36;
        double r3104980 = 1.3141745343712155e+27;
        double r3104981 = 333.75;
        double r3104982 = r3104980 * r3104981;
        double r3104983 = r3104979 + r3104982;
        double r3104984 = r3104983 * r3104983;
        double r3104985 = 1.4394747892125385e+36;
        double r3104986 = 5.5;
        double r3104987 = r3104985 * r3104986;
        double r3104988 = r3104987 * r3104987;
        double r3104989 = r3104984 - r3104988;
        double r3104990 = log(r3104989);
        double r3104991 = cbrt(r3104990);
        double r3104992 = r3104991 * r3104991;
        double r3104993 = exp(r3104992);
        double r3104994 = pow(r3104993, r3104991);
        double r3104995 = /* ERROR: no posit support in C */;
        double r3104996 = /* ERROR: no posit support in C */;
        double r3104997 = r3104979 + r3104996;
        double r3104998 = r3104997 - r3104987;
        double r3104999 = r3104994 / r3104998;
        double r3105000 = r3104978 + r3104999;
        return r3105000;
}

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 2019168 
(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))))