Average Error: 58.1 → 58.1
Time: 2.6s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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 r49405 = 333.75;
        double r49406 = 33096.0;
        double r49407 = 6.0;
        double r49408 = pow(r49406, r49407);
        double r49409 = r49405 * r49408;
        double r49410 = 77617.0;
        double r49411 = r49410 * r49410;
        double r49412 = 11.0;
        double r49413 = r49412 * r49411;
        double r49414 = r49406 * r49406;
        double r49415 = r49413 * r49414;
        double r49416 = -r49408;
        double r49417 = r49415 + r49416;
        double r49418 = -121.0;
        double r49419 = 4.0;
        double r49420 = pow(r49406, r49419);
        double r49421 = r49418 * r49420;
        double r49422 = r49417 + r49421;
        double r49423 = -2.0;
        double r49424 = r49422 + r49423;
        double r49425 = r49411 * r49424;
        double r49426 = r49409 + r49425;
        double r49427 = 5.5;
        double r49428 = 8.0;
        double r49429 = pow(r49406, r49428);
        double r49430 = r49427 * r49429;
        double r49431 = r49426 + r49430;
        double r49432 = 2.0;
        double r49433 = r49432 * r49406;
        double r49434 = r49410 / r49433;
        double r49435 = r49431 + r49434;
        return r49435;
}
↓
double f() {
        double r49436 = 77617.0;
        double r49437 = 11.0;
        double r49438 = r49436 * r49436;
        double r49439 = r49437 * r49438;
        double r49440 = 33096.0;
        double r49441 = r49440 * r49440;
        double r49442 = r49439 * r49441;
        double r49443 = 6.0;
        double r49444 = pow(r49440, r49443);
        double r49445 = 4.0;
        double r49446 = pow(r49440, r49445);
        double r49447 = -121.0;
        double r49448 = -2.0;
        double r49449 = fma(r49446, r49447, r49448);
        double r49450 = r49444 - r49449;
        double r49451 = r49442 - r49450;
        double r49452 = r49436 * r49451;
        double r49453 = 333.75;
        double r49454 = 8.0;
        double r49455 = pow(r49440, r49454);
        double r49456 = 5.5;
        double r49457 = 2.0;
        double r49458 = r49457 * r49440;
        double r49459 = r49436 / r49458;
        double r49460 = fma(r49455, r49456, r49459);
        double r49461 = fma(r49453, r49444, r49460);
        double r49462 = fma(r49436, r49452, r49461);
        return r49462;
}

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 2019353 +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))))