Average Error: 58.1 → 58.1
Time: 16.4s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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 r37469 = 333.75;
        double r37470 = 33096.0;
        double r37471 = 6.0;
        double r37472 = pow(r37470, r37471);
        double r37473 = r37469 * r37472;
        double r37474 = 77617.0;
        double r37475 = r37474 * r37474;
        double r37476 = 11.0;
        double r37477 = r37476 * r37475;
        double r37478 = r37470 * r37470;
        double r37479 = r37477 * r37478;
        double r37480 = -r37472;
        double r37481 = r37479 + r37480;
        double r37482 = -121.0;
        double r37483 = 4.0;
        double r37484 = pow(r37470, r37483);
        double r37485 = r37482 * r37484;
        double r37486 = r37481 + r37485;
        double r37487 = -2.0;
        double r37488 = r37486 + r37487;
        double r37489 = r37475 * r37488;
        double r37490 = r37473 + r37489;
        double r37491 = 5.5;
        double r37492 = 8.0;
        double r37493 = pow(r37470, r37492);
        double r37494 = r37491 * r37493;
        double r37495 = r37490 + r37494;
        double r37496 = 2.0;
        double r37497 = r37496 * r37470;
        double r37498 = r37474 / r37497;
        double r37499 = r37495 + r37498;
        return r37499;
}
↓
double f() {
        double r37500 = 77617.0;
        double r37501 = r37500 * r37500;
        double r37502 = -2.0;
        double r37503 = -121.0;
        double r37504 = 33096.0;
        double r37505 = 4.0;
        double r37506 = pow(r37504, r37505);
        double r37507 = 11.0;
        double r37508 = r37507 * r37501;
        double r37509 = r37504 * r37504;
        double r37510 = r37508 * r37509;
        double r37511 = 6.0;
        double r37512 = pow(r37504, r37511);
        double r37513 = r37510 - r37512;
        double r37514 = fma(r37503, r37506, r37513);
        double r37515 = r37502 + r37514;
        double r37516 = 333.75;
        double r37517 = 5.5;
        double r37518 = 8.0;
        double r37519 = pow(r37504, r37518);
        double r37520 = 2.0;
        double r37521 = r37520 * r37504;
        double r37522 = r37500 / r37521;
        double r37523 = fma(r37517, r37519, r37522);
        double r37524 = fma(r37512, r37516, r37523);
        double r37525 = fma(r37501, r37515, r37524);
        return r37525;
}

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 2019326 +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))))