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 r45423 = 333.75;
        double r45424 = 33096.0;
        double r45425 = 6.0;
        double r45426 = pow(r45424, r45425);
        double r45427 = r45423 * r45426;
        double r45428 = 77617.0;
        double r45429 = r45428 * r45428;
        double r45430 = 11.0;
        double r45431 = r45430 * r45429;
        double r45432 = r45424 * r45424;
        double r45433 = r45431 * r45432;
        double r45434 = -r45426;
        double r45435 = r45433 + r45434;
        double r45436 = -121.0;
        double r45437 = 4.0;
        double r45438 = pow(r45424, r45437);
        double r45439 = r45436 * r45438;
        double r45440 = r45435 + r45439;
        double r45441 = -2.0;
        double r45442 = r45440 + r45441;
        double r45443 = r45429 * r45442;
        double r45444 = r45427 + r45443;
        double r45445 = 5.5;
        double r45446 = 8.0;
        double r45447 = pow(r45424, r45446);
        double r45448 = r45445 * r45447;
        double r45449 = r45444 + r45448;
        double r45450 = 2.0;
        double r45451 = r45450 * r45424;
        double r45452 = r45428 / r45451;
        double r45453 = r45449 + r45452;
        return r45453;
}
↓
double f() {
        double r45454 = 77617.0;
        double r45455 = 11.0;
        double r45456 = r45454 * r45454;
        double r45457 = r45455 * r45456;
        double r45458 = 33096.0;
        double r45459 = r45458 * r45458;
        double r45460 = r45457 * r45459;
        double r45461 = 6.0;
        double r45462 = pow(r45458, r45461);
        double r45463 = 4.0;
        double r45464 = pow(r45458, r45463);
        double r45465 = -121.0;
        double r45466 = -2.0;
        double r45467 = fma(r45464, r45465, r45466);
        double r45468 = r45462 - r45467;
        double r45469 = r45460 - r45468;
        double r45470 = r45454 * r45469;
        double r45471 = 333.75;
        double r45472 = 8.0;
        double r45473 = pow(r45458, r45472);
        double r45474 = 5.5;
        double r45475 = 2.0;
        double r45476 = r45475 * r45458;
        double r45477 = r45454 / r45476;
        double r45478 = fma(r45473, r45474, r45477);
        double r45479 = fma(r45471, r45462, r45478);
        double r45480 = fma(r45454, r45470, r45479);
        return r45480;
}

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 2020025 +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))))