Average Error: 5.9 → 1.8
Time: 7.4s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 1.408347514255849598590216064760682864053 \cdot 10^{307}\right):\\ \;\;\;\;\left(\left(\left(x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;\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 = -\infty \lor \neg \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 \le 1.408347514255849598590216064760682864053 \cdot 10^{307}\right):\\
\;\;\;\;\left(\left(\left(x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\right) - \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)\\

\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 r119509 = x;
        double r119510 = 18.0;
        double r119511 = r119509 * r119510;
        double r119512 = y;
        double r119513 = r119511 * r119512;
        double r119514 = z;
        double r119515 = r119513 * r119514;
        double r119516 = t;
        double r119517 = r119515 * r119516;
        double r119518 = a;
        double r119519 = 4.0;
        double r119520 = r119518 * r119519;
        double r119521 = r119520 * r119516;
        double r119522 = r119517 - r119521;
        double r119523 = b;
        double r119524 = c;
        double r119525 = r119523 * r119524;
        double r119526 = r119522 + r119525;
        double r119527 = r119509 * r119519;
        double r119528 = i;
        double r119529 = r119527 * r119528;
        double r119530 = r119526 - r119529;
        double r119531 = j;
        double r119532 = 27.0;
        double r119533 = r119531 * r119532;
        double r119534 = k;
        double r119535 = r119533 * r119534;
        double r119536 = r119530 - r119535;
        return r119536;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r119537 = x;
        double r119538 = 18.0;
        double r119539 = r119537 * r119538;
        double r119540 = y;
        double r119541 = r119539 * r119540;
        double r119542 = z;
        double r119543 = r119541 * r119542;
        double r119544 = t;
        double r119545 = r119543 * r119544;
        double r119546 = a;
        double r119547 = 4.0;
        double r119548 = r119546 * r119547;
        double r119549 = r119548 * r119544;
        double r119550 = r119545 - r119549;
        double r119551 = b;
        double r119552 = c;
        double r119553 = r119551 * r119552;
        double r119554 = r119550 + r119553;
        double r119555 = r119537 * r119547;
        double r119556 = i;
        double r119557 = r119555 * r119556;
        double r119558 = r119554 - r119557;
        double r119559 = -inf.0;
        bool r119560 = r119558 <= r119559;
        double r119561 = 1.4083475142558496e+307;
        bool r119562 = r119558 <= r119561;
        double r119563 = !r119562;
        bool r119564 = r119560 || r119563;
        double r119565 = r119540 * r119542;
        double r119566 = r119538 * r119565;
        double r119567 = r119566 * r119544;
        double r119568 = r119537 * r119567;
        double r119569 = r119568 - r119549;
        double r119570 = r119569 + r119553;
        double r119571 = r119570 - r119557;
        double r119572 = j;
        double r119573 = 27.0;
        double r119574 = k;
        double r119575 = r119573 * r119574;
        double r119576 = r119572 * r119575;
        double r119577 = r119571 - r119576;
        double r119578 = r119558 - r119576;
        double r119579 = r119564 ? r119577 : r119578;
        return r119579;
}

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 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0 or 1.4083475142558496e+307 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 63.0

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

    3. Applied associate-*l*40.5

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

    5. Applied associate-*l*40.2

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

    7. Applied associate-*l*40.3

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

    9. Applied associate-*l*16.8

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

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 1.4083475142558496e+307

    1. Initial program 0.3

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

    3. Applied associate-*l*0.3

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 1.408347514255849598590216064760682864053 \cdot 10^{307}\right):\\ \;\;\;\;\left(\left(\left(x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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)))