Average Error: 5.2 → 3.5
Time: 36.2s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.5865933573833304 \cdot 10^{+54}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(z \cdot 18.0\right) \cdot \left(y \cdot x\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \le 1.4118953814768603 \cdot 10^{-19}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(t \cdot \left(\left(y \cdot z\right) \cdot x\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(\left(18.0 \cdot x\right) \cdot y\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.5865933573833304 \cdot 10^{+54}:\\
\;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(z \cdot 18.0\right) \cdot \left(y \cdot x\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\

\mathbf{elif}\;z \le 1.4118953814768603 \cdot 10^{-19}:\\
\;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(t \cdot \left(\left(y \cdot z\right) \cdot x\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(\left(18.0 \cdot x\right) \cdot y\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \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 r1989405 = x;
        double r1989406 = 18.0;
        double r1989407 = r1989405 * r1989406;
        double r1989408 = y;
        double r1989409 = r1989407 * r1989408;
        double r1989410 = z;
        double r1989411 = r1989409 * r1989410;
        double r1989412 = t;
        double r1989413 = r1989411 * r1989412;
        double r1989414 = a;
        double r1989415 = 4.0;
        double r1989416 = r1989414 * r1989415;
        double r1989417 = r1989416 * r1989412;
        double r1989418 = r1989413 - r1989417;
        double r1989419 = b;
        double r1989420 = c;
        double r1989421 = r1989419 * r1989420;
        double r1989422 = r1989418 + r1989421;
        double r1989423 = r1989405 * r1989415;
        double r1989424 = i;
        double r1989425 = r1989423 * r1989424;
        double r1989426 = r1989422 - r1989425;
        double r1989427 = j;
        double r1989428 = 27.0;
        double r1989429 = r1989427 * r1989428;
        double r1989430 = k;
        double r1989431 = r1989429 * r1989430;
        double r1989432 = r1989426 - r1989431;
        return r1989432;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r1989433 = z;
        double r1989434 = -1.5865933573833304e+54;
        bool r1989435 = r1989433 <= r1989434;
        double r1989436 = b;
        double r1989437 = c;
        double r1989438 = r1989436 * r1989437;
        double r1989439 = t;
        double r1989440 = 18.0;
        double r1989441 = r1989433 * r1989440;
        double r1989442 = y;
        double r1989443 = x;
        double r1989444 = r1989442 * r1989443;
        double r1989445 = r1989441 * r1989444;
        double r1989446 = r1989439 * r1989445;
        double r1989447 = a;
        double r1989448 = 4.0;
        double r1989449 = r1989447 * r1989448;
        double r1989450 = r1989439 * r1989449;
        double r1989451 = r1989446 - r1989450;
        double r1989452 = r1989438 + r1989451;
        double r1989453 = r1989443 * r1989448;
        double r1989454 = i;
        double r1989455 = r1989453 * r1989454;
        double r1989456 = r1989452 - r1989455;
        double r1989457 = 27.0;
        double r1989458 = j;
        double r1989459 = k;
        double r1989460 = r1989458 * r1989459;
        double r1989461 = r1989457 * r1989460;
        double r1989462 = r1989456 - r1989461;
        double r1989463 = 1.4118953814768603e-19;
        bool r1989464 = r1989433 <= r1989463;
        double r1989465 = r1989442 * r1989433;
        double r1989466 = r1989465 * r1989443;
        double r1989467 = r1989439 * r1989466;
        double r1989468 = r1989440 * r1989467;
        double r1989469 = r1989468 - r1989450;
        double r1989470 = r1989438 + r1989469;
        double r1989471 = r1989470 - r1989455;
        double r1989472 = r1989471 - r1989461;
        double r1989473 = r1989440 * r1989443;
        double r1989474 = r1989473 * r1989442;
        double r1989475 = r1989433 * r1989474;
        double r1989476 = r1989439 * r1989475;
        double r1989477 = r1989476 - r1989450;
        double r1989478 = r1989438 + r1989477;
        double r1989479 = r1989478 - r1989455;
        double r1989480 = r1989457 * r1989459;
        double r1989481 = r1989458 * r1989480;
        double r1989482 = r1989479 - r1989481;
        double r1989483 = r1989464 ? r1989472 : r1989482;
        double r1989484 = r1989435 ? r1989462 : r1989483;
        return r1989484;
}

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 3 regimes

  2. if z < -1.5865933573833304e+54

    1. Initial program 7.3

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Taylor expanded around 0 7.2

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{27.0 \cdot \left(j \cdot k\right)}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity7.2

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    5. Applied associate-*r*7.2

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot 1\right) \cdot t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    6. Simplified7.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(y \cdot x\right) \cdot \left(18.0 \cdot z\right)\right)} \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    if -1.5865933573833304e+54 < z < 1.4118953814768603e-19

    1. Initial program 4.2

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Taylor expanded around 0 4.2

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{27.0 \cdot \left(j \cdot k\right)}\]

    3. Taylor expanded around inf 1.2

      \[\leadsto \left(\left(\left(\color{blue}{18.0 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    if 1.4118953814768603e-19 < z

    1. Initial program 6.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*6.3

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.5865933573833304 \cdot 10^{+54}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(z \cdot 18.0\right) \cdot \left(y \cdot x\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \le 1.4118953814768603 \cdot 10^{-19}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(t \cdot \left(\left(y \cdot z\right) \cdot x\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(\left(18.0 \cdot x\right) \cdot y\right)\right) - t \cdot \left(a \cdot 4.0\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))