Average Error: 58.1 → 63.6
Time: 32.4s
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 r3669416 = 333.75;
        double r3669417 = 33096.0;
        double r3669418 = 6.0;
        double r3669419 = pow(r3669417, r3669418);
        double r3669420 = r3669416 * r3669419;
        double r3669421 = 77617.0;
        double r3669422 = r3669421 * r3669421;
        double r3669423 = 11.0;
        double r3669424 = r3669423 * r3669422;
        double r3669425 = r3669417 * r3669417;
        double r3669426 = r3669424 * r3669425;
        double r3669427 = -r3669419;
        double r3669428 = r3669426 + r3669427;
        double r3669429 = -121.0;
        double r3669430 = 4.0;
        double r3669431 = pow(r3669417, r3669430);
        double r3669432 = r3669429 * r3669431;
        double r3669433 = r3669428 + r3669432;
        double r3669434 = -2.0;
        double r3669435 = r3669433 + r3669434;
        double r3669436 = r3669422 * r3669435;
        double r3669437 = r3669420 + r3669436;
        double r3669438 = 5.5;
        double r3669439 = 8.0;
        double r3669440 = pow(r3669417, r3669439);
        double r3669441 = r3669438 * r3669440;
        double r3669442 = r3669437 + r3669441;
        double r3669443 = 2.0;
        double r3669444 = r3669443 * r3669417;
        double r3669445 = r3669421 / r3669444;
        double r3669446 = r3669442 + r3669445;
        return r3669446;
}
↓
double f() {
        double r3669447 = 1.1726039400531787;
        double r3669448 = -7.917111779274712e+36;
        double r3669449 = 1.3141745343712155e+27;
        double r3669450 = 333.75;
        double r3669451 = r3669449 * r3669450;
        double r3669452 = r3669448 + r3669451;
        double r3669453 = r3669452 * r3669452;
        double r3669454 = 1.4394747892125385e+36;
        double r3669455 = 5.5;
        double r3669456 = r3669454 * r3669455;
        double r3669457 = r3669456 * r3669456;
        double r3669458 = r3669453 - r3669457;
        double r3669459 = log(r3669458);
        double r3669460 = cbrt(r3669459);
        double r3669461 = r3669460 * r3669460;
        double r3669462 = exp(r3669461);
        double r3669463 = pow(r3669462, r3669460);
        double r3669464 = /* ERROR: no posit support in C */;
        double r3669465 = /* ERROR: no posit support in C */;
        double r3669466 = r3669448 + r3669465;
        double r3669467 = r3669466 - r3669456;
        double r3669468 = r3669463 / r3669467;
        double r3669469 = r3669447 + r3669468;
        return r3669469;
}

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 2019144 
(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))))