Average Error: 5.7 → 2.1
Time: 7.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5489127871.7275047 \lor \neg \left(x \le 1.3012924431466324 \cdot 10^{-48}\right):\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;x \le -5489127871.7275047 \lor \neg \left(x \le 1.3012924431466324 \cdot 10^{-48}\right):\\
\;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r127466 = x;
        double r127467 = 18.0;
        double r127468 = r127466 * r127467;
        double r127469 = y;
        double r127470 = r127468 * r127469;
        double r127471 = z;
        double r127472 = r127470 * r127471;
        double r127473 = t;
        double r127474 = r127472 * r127473;
        double r127475 = a;
        double r127476 = 4.0;
        double r127477 = r127475 * r127476;
        double r127478 = r127477 * r127473;
        double r127479 = r127474 - r127478;
        double r127480 = b;
        double r127481 = c;
        double r127482 = r127480 * r127481;
        double r127483 = r127479 + r127482;
        double r127484 = r127466 * r127476;
        double r127485 = i;
        double r127486 = r127484 * r127485;
        double r127487 = r127483 - r127486;
        double r127488 = j;
        double r127489 = 27.0;
        double r127490 = r127488 * r127489;
        double r127491 = k;
        double r127492 = r127490 * r127491;
        double r127493 = r127487 - r127492;
        return r127493;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r127494 = x;
        double r127495 = -5489127871.727505;
        bool r127496 = r127494 <= r127495;
        double r127497 = 1.3012924431466324e-48;
        bool r127498 = r127494 <= r127497;
        double r127499 = !r127498;
        bool r127500 = r127496 || r127499;
        double r127501 = 18.0;
        double r127502 = r127494 * r127501;
        double r127503 = y;
        double r127504 = z;
        double r127505 = r127503 * r127504;
        double r127506 = t;
        double r127507 = r127505 * r127506;
        double r127508 = r127502 * r127507;
        double r127509 = a;
        double r127510 = 4.0;
        double r127511 = r127509 * r127510;
        double r127512 = r127511 * r127506;
        double r127513 = r127508 - r127512;
        double r127514 = b;
        double r127515 = c;
        double r127516 = r127514 * r127515;
        double r127517 = r127513 + r127516;
        double r127518 = r127494 * r127510;
        double r127519 = i;
        double r127520 = r127518 * r127519;
        double r127521 = r127517 - r127520;
        double r127522 = j;
        double r127523 = 27.0;
        double r127524 = r127522 * r127523;
        double r127525 = k;
        double r127526 = r127524 * r127525;
        double r127527 = r127521 - r127526;
        double r127528 = r127502 * r127503;
        double r127529 = r127528 * r127504;
        double r127530 = r127529 * r127506;
        double r127531 = r127530 - r127512;
        double r127532 = r127531 + r127516;
        double r127533 = r127532 - r127520;
        double r127534 = r127523 * r127525;
        double r127535 = r127522 * r127534;
        double r127536 = r127533 - r127535;
        double r127537 = r127500 ? r127527 : r127536;
        return r127537;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -5489127871.727505 or 1.3012924431466324e-48 < x

    1. Initial program 11.5

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*6.8

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    4. Using strategy rm

    5. Applied associate-*l*2.6

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    if -5489127871.727505 < x < 1.3012924431466324e-48

    1. Initial program 1.8

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*1.8

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{j \cdot \left(27 \cdot k\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5489127871.7275047 \lor \neg \left(x \le 1.3012924431466324 \cdot 10^{-48}\right):\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))