Average Error: 58.1 → 56.8
Time: 33.1s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\frac{\left(\left(\mathsf{fma}\left(5.5, {33096}^{8}, \mathsf{fma}\left(77617 \cdot \mathsf{fma}\left({33096}^{4}, -121, \left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) - {33096}^{6}\right) + -2\right), 77617, {33096}^{6} \cdot 333.75\right)\right)\right)\right) \cdot \left(\left(\mathsf{fma}\left(5.5, {33096}^{8}, \mathsf{fma}\left(77617 \cdot \mathsf{fma}\left({33096}^{4}, -121, \left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) - {33096}^{6}\right) + -2\right), 77617, {33096}^{6} \cdot 333.75\right)\right)\right)\right) - \frac{77617}{2 \cdot 33096} \cdot \frac{77617}{2 \cdot 33096}}{\left(\left(\mathsf{fma}\left(5.5, {33096}^{8}, \mathsf{fma}\left(77617 \cdot \mathsf{fma}\left({33096}^{4}, -121, \left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) - {33096}^{6}\right) + -2\right), 77617, {33096}^{6} \cdot 333.75\right)\right)\right)\right) - \frac{77617}{2 \cdot 33096}}\]
\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{\left(\left(\mathsf{fma}\left(5.5, {33096}^{8}, \mathsf{fma}\left(77617 \cdot \mathsf{fma}\left({33096}^{4}, -121, \left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) - {33096}^{6}\right) + -2\right), 77617, {33096}^{6} \cdot 333.75\right)\right)\right)\right) \cdot \left(\left(\mathsf{fma}\left(5.5, {33096}^{8}, \mathsf{fma}\left(77617 \cdot \mathsf{fma}\left({33096}^{4}, -121, \left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) - {33096}^{6}\right) + -2\right), 77617, {33096}^{6} \cdot 333.75\right)\right)\right)\right) - \frac{77617}{2 \cdot 33096} \cdot \frac{77617}{2 \cdot 33096}}{\left(\left(\mathsf{fma}\left(5.5, {33096}^{8}, \mathsf{fma}\left(77617 \cdot \mathsf{fma}\left({33096}^{4}, -121, \left(11 \cdot \left(\left(33096 \cdot 77617\right) \cdot \left(33096 \cdot 77617\right)\right) - {33096}^{6}\right) + -2\right), 77617, {33096}^{6} \cdot 333.75\right)\right)\right)\right) - \frac{77617}{2 \cdot 33096}}
double f() {
        double r3251429 = 333.75;
        double r3251430 = 33096.0;
        double r3251431 = 6.0;
        double r3251432 = pow(r3251430, r3251431);
        double r3251433 = r3251429 * r3251432;
        double r3251434 = 77617.0;
        double r3251435 = r3251434 * r3251434;
        double r3251436 = 11.0;
        double r3251437 = r3251436 * r3251435;
        double r3251438 = r3251430 * r3251430;
        double r3251439 = r3251437 * r3251438;
        double r3251440 = -r3251432;
        double r3251441 = r3251439 + r3251440;
        double r3251442 = -121.0;
        double r3251443 = 4.0;
        double r3251444 = pow(r3251430, r3251443);
        double r3251445 = r3251442 * r3251444;
        double r3251446 = r3251441 + r3251445;
        double r3251447 = -2.0;
        double r3251448 = r3251446 + r3251447;
        double r3251449 = r3251435 * r3251448;
        double r3251450 = r3251433 + r3251449;
        double r3251451 = 5.5;
        double r3251452 = 8.0;
        double r3251453 = pow(r3251430, r3251452);
        double r3251454 = r3251451 * r3251453;
        double r3251455 = r3251450 + r3251454;
        double r3251456 = 2.0;
        double r3251457 = r3251456 * r3251430;
        double r3251458 = r3251434 / r3251457;
        double r3251459 = r3251455 + r3251458;
        return r3251459;
}
↓
double f() {
        double r3251460 = 5.5;
        double r3251461 = 33096.0;
        double r3251462 = 8.0;
        double r3251463 = pow(r3251461, r3251462);
        double r3251464 = 77617.0;
        double r3251465 = 4.0;
        double r3251466 = pow(r3251461, r3251465);
        double r3251467 = -121.0;
        double r3251468 = 11.0;
        double r3251469 = r3251461 * r3251464;
        double r3251470 = r3251469 * r3251469;
        double r3251471 = r3251468 * r3251470;
        double r3251472 = 6.0;
        double r3251473 = pow(r3251461, r3251472);
        double r3251474 = r3251471 - r3251473;
        double r3251475 = -2.0;
        double r3251476 = r3251474 + r3251475;
        double r3251477 = fma(r3251466, r3251467, r3251476);
        double r3251478 = r3251464 * r3251477;
        double r3251479 = 333.75;
        double r3251480 = r3251473 * r3251479;
        double r3251481 = fma(r3251478, r3251464, r3251480);
        double r3251482 = fma(r3251460, r3251463, r3251481);
        double r3251483 = /* ERROR: no posit support in C */;
        double r3251484 = /* ERROR: no posit support in C */;
        double r3251485 = r3251484 * r3251484;
        double r3251486 = 2.0;
        double r3251487 = r3251486 * r3251461;
        double r3251488 = r3251464 / r3251487;
        double r3251489 = r3251488 * r3251488;
        double r3251490 = r3251485 - r3251489;
        double r3251491 = r3251484 - r3251488;
        double r3251492 = r3251490 / r3251491;
        return r3251492;
}

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

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

  6. Applied flip-+56.8

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

  7. Final simplification56.8

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))))