Average Error: 58.1 → 63.6
Time: 19.6s
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 r1125489 = 333.75;
        double r1125490 = 33096.0;
        double r1125491 = 6.0;
        double r1125492 = pow(r1125490, r1125491);
        double r1125493 = r1125489 * r1125492;
        double r1125494 = 77617.0;
        double r1125495 = r1125494 * r1125494;
        double r1125496 = 11.0;
        double r1125497 = r1125496 * r1125495;
        double r1125498 = r1125490 * r1125490;
        double r1125499 = r1125497 * r1125498;
        double r1125500 = -r1125492;
        double r1125501 = r1125499 + r1125500;
        double r1125502 = -121.0;
        double r1125503 = 4.0;
        double r1125504 = pow(r1125490, r1125503);
        double r1125505 = r1125502 * r1125504;
        double r1125506 = r1125501 + r1125505;
        double r1125507 = -2.0;
        double r1125508 = r1125506 + r1125507;
        double r1125509 = r1125495 * r1125508;
        double r1125510 = r1125493 + r1125509;
        double r1125511 = 5.5;
        double r1125512 = 8.0;
        double r1125513 = pow(r1125490, r1125512);
        double r1125514 = r1125511 * r1125513;
        double r1125515 = r1125510 + r1125514;
        double r1125516 = 2.0;
        double r1125517 = r1125516 * r1125490;
        double r1125518 = r1125494 / r1125517;
        double r1125519 = r1125515 + r1125518;
        return r1125519;
}
↓
double f() {
        double r1125520 = 1.1726039400531787;
        double r1125521 = -7.917111779274712e+36;
        double r1125522 = 1.3141745343712155e+27;
        double r1125523 = 333.75;
        double r1125524 = r1125522 * r1125523;
        double r1125525 = r1125521 + r1125524;
        double r1125526 = r1125525 * r1125525;
        double r1125527 = 1.4394747892125385e+36;
        double r1125528 = 5.5;
        double r1125529 = r1125527 * r1125528;
        double r1125530 = r1125529 * r1125529;
        double r1125531 = r1125526 - r1125530;
        double r1125532 = log(r1125531);
        double r1125533 = cbrt(r1125532);
        double r1125534 = r1125533 * r1125533;
        double r1125535 = exp(r1125534);
        double r1125536 = pow(r1125535, r1125533);
        double r1125537 = /* ERROR: no posit support in C */;
        double r1125538 = /* ERROR: no posit support in C */;
        double r1125539 = r1125521 + r1125538;
        double r1125540 = r1125539 - r1125529;
        double r1125541 = r1125536 / r1125540;
        double r1125542 = r1125520 + r1125541;
        return r1125542;
}

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 2019152 
(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))))