Average Error: 58.1 → 63.6
Time: 21.9s
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 r2796456 = 333.75;
        double r2796457 = 33096.0;
        double r2796458 = 6.0;
        double r2796459 = pow(r2796457, r2796458);
        double r2796460 = r2796456 * r2796459;
        double r2796461 = 77617.0;
        double r2796462 = r2796461 * r2796461;
        double r2796463 = 11.0;
        double r2796464 = r2796463 * r2796462;
        double r2796465 = r2796457 * r2796457;
        double r2796466 = r2796464 * r2796465;
        double r2796467 = -r2796459;
        double r2796468 = r2796466 + r2796467;
        double r2796469 = -121.0;
        double r2796470 = 4.0;
        double r2796471 = pow(r2796457, r2796470);
        double r2796472 = r2796469 * r2796471;
        double r2796473 = r2796468 + r2796472;
        double r2796474 = -2.0;
        double r2796475 = r2796473 + r2796474;
        double r2796476 = r2796462 * r2796475;
        double r2796477 = r2796460 + r2796476;
        double r2796478 = 5.5;
        double r2796479 = 8.0;
        double r2796480 = pow(r2796457, r2796479);
        double r2796481 = r2796478 * r2796480;
        double r2796482 = r2796477 + r2796481;
        double r2796483 = 2.0;
        double r2796484 = r2796483 * r2796457;
        double r2796485 = r2796461 / r2796484;
        double r2796486 = r2796482 + r2796485;
        return r2796486;
}
↓
double f() {
        double r2796487 = 1.1726039400531787;
        double r2796488 = -7.917111779274712e+36;
        double r2796489 = 1.3141745343712155e+27;
        double r2796490 = 333.75;
        double r2796491 = r2796489 * r2796490;
        double r2796492 = r2796488 + r2796491;
        double r2796493 = r2796492 * r2796492;
        double r2796494 = 1.4394747892125385e+36;
        double r2796495 = 5.5;
        double r2796496 = r2796494 * r2796495;
        double r2796497 = r2796496 * r2796496;
        double r2796498 = r2796493 - r2796497;
        double r2796499 = log(r2796498);
        double r2796500 = cbrt(r2796499);
        double r2796501 = r2796500 * r2796500;
        double r2796502 = exp(r2796501);
        double r2796503 = pow(r2796502, r2796500);
        double r2796504 = /* ERROR: no posit support in C */;
        double r2796505 = /* ERROR: no posit support in C */;
        double r2796506 = r2796488 + r2796505;
        double r2796507 = r2796506 - r2796496;
        double r2796508 = r2796503 / r2796507;
        double r2796509 = r2796487 + r2796508;
        return r2796509;
}

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 2019163 
(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))))