Average Error: 5.9 → 2.1
Time: 6.9s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.1318127710871948 \cdot 10^{-10} \lor \neg \left(x \le 52701.756950327122\right):\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]
\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 -9.1318127710871948 \cdot 10^{-10} \lor \neg \left(x \le 52701.756950327122\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(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\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\\

\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 r139399 = x;
        double r139400 = 18.0;
        double r139401 = r139399 * r139400;
        double r139402 = y;
        double r139403 = r139401 * r139402;
        double r139404 = z;
        double r139405 = r139403 * r139404;
        double r139406 = t;
        double r139407 = r139405 * r139406;
        double r139408 = a;
        double r139409 = 4.0;
        double r139410 = r139408 * r139409;
        double r139411 = r139410 * r139406;
        double r139412 = r139407 - r139411;
        double r139413 = b;
        double r139414 = c;
        double r139415 = r139413 * r139414;
        double r139416 = r139412 + r139415;
        double r139417 = r139399 * r139409;
        double r139418 = i;
        double r139419 = r139417 * r139418;
        double r139420 = r139416 - r139419;
        double r139421 = j;
        double r139422 = 27.0;
        double r139423 = r139421 * r139422;
        double r139424 = k;
        double r139425 = r139423 * r139424;
        double r139426 = r139420 - r139425;
        return r139426;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r139427 = x;
        double r139428 = -9.131812771087195e-10;
        bool r139429 = r139427 <= r139428;
        double r139430 = 52701.75695032712;
        bool r139431 = r139427 <= r139430;
        double r139432 = !r139431;
        bool r139433 = r139429 || r139432;
        double r139434 = 18.0;
        double r139435 = r139427 * r139434;
        double r139436 = y;
        double r139437 = z;
        double r139438 = r139436 * r139437;
        double r139439 = t;
        double r139440 = r139438 * r139439;
        double r139441 = r139435 * r139440;
        double r139442 = a;
        double r139443 = 4.0;
        double r139444 = r139442 * r139443;
        double r139445 = r139444 * r139439;
        double r139446 = r139441 - r139445;
        double r139447 = b;
        double r139448 = c;
        double r139449 = r139447 * r139448;
        double r139450 = r139446 + r139449;
        double r139451 = r139427 * r139443;
        double r139452 = i;
        double r139453 = r139451 * r139452;
        double r139454 = r139450 - r139453;
        double r139455 = j;
        double r139456 = 27.0;
        double r139457 = r139455 * r139456;
        double r139458 = k;
        double r139459 = r139457 * r139458;
        double r139460 = r139454 - r139459;
        double r139461 = r139435 * r139436;
        double r139462 = cbrt(r139461);
        double r139463 = r139462 * r139462;
        double r139464 = r139463 * r139462;
        double r139465 = r139464 * r139437;
        double r139466 = r139465 * r139439;
        double r139467 = r139466 - r139445;
        double r139468 = r139467 + r139449;
        double r139469 = r139468 - r139453;
        double r139470 = r139469 - r139459;
        double r139471 = r139433 ? r139460 : r139470;
        return r139471;
}

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 < -9.131812771087195e-10 or 52701.75695032712 < x

    1. Initial program 12.2

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

    3. Applied associate-*l*7.4

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

    5. Applied associate-*l*2.2

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

    if -9.131812771087195e-10 < x < 52701.75695032712

    1. Initial program 1.9

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

    3. Applied add-cube-cbrt2.0

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.1318127710871948 \cdot 10^{-10} \lor \neg \left(x \le 52701.756950327122\right):\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(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)))