Average Error: 58.1 → 58.1
Time: 2.5s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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}
↓
\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)
double f() {
        double r41420 = 333.75;
        double r41421 = 33096.0;
        double r41422 = 6.0;
        double r41423 = pow(r41421, r41422);
        double r41424 = r41420 * r41423;
        double r41425 = 77617.0;
        double r41426 = r41425 * r41425;
        double r41427 = 11.0;
        double r41428 = r41427 * r41426;
        double r41429 = r41421 * r41421;
        double r41430 = r41428 * r41429;
        double r41431 = -r41423;
        double r41432 = r41430 + r41431;
        double r41433 = -121.0;
        double r41434 = 4.0;
        double r41435 = pow(r41421, r41434);
        double r41436 = r41433 * r41435;
        double r41437 = r41432 + r41436;
        double r41438 = -2.0;
        double r41439 = r41437 + r41438;
        double r41440 = r41426 * r41439;
        double r41441 = r41424 + r41440;
        double r41442 = 5.5;
        double r41443 = 8.0;
        double r41444 = pow(r41421, r41443);
        double r41445 = r41442 * r41444;
        double r41446 = r41441 + r41445;
        double r41447 = 2.0;
        double r41448 = r41447 * r41421;
        double r41449 = r41425 / r41448;
        double r41450 = r41446 + r41449;
        return r41450;
}
↓
double f() {
        double r41451 = 77617.0;
        double r41452 = 11.0;
        double r41453 = r41451 * r41451;
        double r41454 = r41452 * r41453;
        double r41455 = 33096.0;
        double r41456 = r41455 * r41455;
        double r41457 = r41454 * r41456;
        double r41458 = 6.0;
        double r41459 = pow(r41455, r41458);
        double r41460 = 4.0;
        double r41461 = pow(r41455, r41460);
        double r41462 = -121.0;
        double r41463 = -2.0;
        double r41464 = fma(r41461, r41462, r41463);
        double r41465 = r41459 - r41464;
        double r41466 = r41457 - r41465;
        double r41467 = r41451 * r41466;
        double r41468 = 333.75;
        double r41469 = 8.0;
        double r41470 = pow(r41455, r41469);
        double r41471 = 5.5;
        double r41472 = 2.0;
        double r41473 = r41472 * r41455;
        double r41474 = r41451 / r41473;
        double r41475 = fma(r41470, r41471, r41474);
        double r41476 = fma(r41468, r41459, r41475);
        double r41477 = fma(r41451, r41467, r41476);
        return r41477;
}

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. Simplified58.1

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

  3. Simplified58.1

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

  4. Final simplification58.1

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 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))))