Average Error: 58.1 → 58.1
Time: 17.2s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)
double f() {
        double r73475 = 333.75;
        double r73476 = 33096.0;
        double r73477 = 6.0;
        double r73478 = pow(r73476, r73477);
        double r73479 = r73475 * r73478;
        double r73480 = 77617.0;
        double r73481 = r73480 * r73480;
        double r73482 = 11.0;
        double r73483 = r73482 * r73481;
        double r73484 = r73476 * r73476;
        double r73485 = r73483 * r73484;
        double r73486 = -r73478;
        double r73487 = r73485 + r73486;
        double r73488 = -121.0;
        double r73489 = 4.0;
        double r73490 = pow(r73476, r73489);
        double r73491 = r73488 * r73490;
        double r73492 = r73487 + r73491;
        double r73493 = -2.0;
        double r73494 = r73492 + r73493;
        double r73495 = r73481 * r73494;
        double r73496 = r73479 + r73495;
        double r73497 = 5.5;
        double r73498 = 8.0;
        double r73499 = pow(r73476, r73498);
        double r73500 = r73497 * r73499;
        double r73501 = r73496 + r73500;
        double r73502 = 2.0;
        double r73503 = r73502 * r73476;
        double r73504 = r73480 / r73503;
        double r73505 = r73501 + r73504;
        return r73505;
}
↓
double f() {
        double r73506 = 77617.0;
        double r73507 = r73506 * r73506;
        double r73508 = -2.0;
        double r73509 = -121.0;
        double r73510 = 33096.0;
        double r73511 = 4.0;
        double r73512 = pow(r73510, r73511);
        double r73513 = 11.0;
        double r73514 = r73513 * r73507;
        double r73515 = r73510 * r73510;
        double r73516 = r73514 * r73515;
        double r73517 = 6.0;
        double r73518 = pow(r73510, r73517);
        double r73519 = r73516 - r73518;
        double r73520 = fma(r73509, r73512, r73519);
        double r73521 = r73508 + r73520;
        double r73522 = 333.75;
        double r73523 = 5.5;
        double r73524 = 8.0;
        double r73525 = pow(r73510, r73524);
        double r73526 = 2.0;
        double r73527 = r73526 * r73510;
        double r73528 = r73506 / r73527;
        double r73529 = fma(r73523, r73525, r73528);
        double r73530 = fma(r73518, r73522, r73529);
        double r73531 = fma(r73507, r73521, r73530);
        return r73531;
}

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

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

  3. Final simplification58.1

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

Reproduce

herbie shell --seed 2019303 +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))))