Average Error: 58.1 → 58.1
Time: 18.7s
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 r29481 = 333.75;
        double r29482 = 33096.0;
        double r29483 = 6.0;
        double r29484 = pow(r29482, r29483);
        double r29485 = r29481 * r29484;
        double r29486 = 77617.0;
        double r29487 = r29486 * r29486;
        double r29488 = 11.0;
        double r29489 = r29488 * r29487;
        double r29490 = r29482 * r29482;
        double r29491 = r29489 * r29490;
        double r29492 = -r29484;
        double r29493 = r29491 + r29492;
        double r29494 = -121.0;
        double r29495 = 4.0;
        double r29496 = pow(r29482, r29495);
        double r29497 = r29494 * r29496;
        double r29498 = r29493 + r29497;
        double r29499 = -2.0;
        double r29500 = r29498 + r29499;
        double r29501 = r29487 * r29500;
        double r29502 = r29485 + r29501;
        double r29503 = 5.5;
        double r29504 = 8.0;
        double r29505 = pow(r29482, r29504);
        double r29506 = r29503 * r29505;
        double r29507 = r29502 + r29506;
        double r29508 = 2.0;
        double r29509 = r29508 * r29482;
        double r29510 = r29486 / r29509;
        double r29511 = r29507 + r29510;
        return r29511;
}
↓
double f() {
        double r29512 = 77617.0;
        double r29513 = r29512 * r29512;
        double r29514 = -2.0;
        double r29515 = -121.0;
        double r29516 = 33096.0;
        double r29517 = 4.0;
        double r29518 = pow(r29516, r29517);
        double r29519 = 11.0;
        double r29520 = r29519 * r29513;
        double r29521 = r29516 * r29516;
        double r29522 = r29520 * r29521;
        double r29523 = 6.0;
        double r29524 = pow(r29516, r29523);
        double r29525 = r29522 - r29524;
        double r29526 = fma(r29515, r29518, r29525);
        double r29527 = r29514 + r29526;
        double r29528 = 333.75;
        double r29529 = 5.5;
        double r29530 = 8.0;
        double r29531 = pow(r29516, r29530);
        double r29532 = 2.0;
        double r29533 = r29532 * r29516;
        double r29534 = r29512 / r29533;
        double r29535 = fma(r29529, r29531, r29534);
        double r29536 = fma(r29524, r29528, r29535);
        double r29537 = fma(r29513, r29527, r29536);
        return r29537;
}

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 2019323 +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))))