Average Error: 5.0 → 4.1
Time: 20.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.442676120004847 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) - 4.0 \cdot \left(a \cdot t\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;t \le 7.540536889545399 \cdot 10^{-05}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot x\right) \cdot y\right) - \left(4.0 \cdot a\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) - 4.0 \cdot \left(a \cdot t\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]
\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}\;t \le -5.442676120004847 \cdot 10^{-262}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) - 4.0 \cdot \left(a \cdot t\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\

\mathbf{elif}\;t \le 7.540536889545399 \cdot 10^{-05}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot x\right) \cdot y\right) - \left(4.0 \cdot a\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) - 4.0 \cdot \left(a \cdot t\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 r1991492 = x;
        double r1991493 = 18.0;
        double r1991494 = r1991492 * r1991493;
        double r1991495 = y;
        double r1991496 = r1991494 * r1991495;
        double r1991497 = z;
        double r1991498 = r1991496 * r1991497;
        double r1991499 = t;
        double r1991500 = r1991498 * r1991499;
        double r1991501 = a;
        double r1991502 = 4.0;
        double r1991503 = r1991501 * r1991502;
        double r1991504 = r1991503 * r1991499;
        double r1991505 = r1991500 - r1991504;
        double r1991506 = b;
        double r1991507 = c;
        double r1991508 = r1991506 * r1991507;
        double r1991509 = r1991505 + r1991508;
        double r1991510 = r1991492 * r1991502;
        double r1991511 = i;
        double r1991512 = r1991510 * r1991511;
        double r1991513 = r1991509 - r1991512;
        double r1991514 = j;
        double r1991515 = 27.0;
        double r1991516 = r1991514 * r1991515;
        double r1991517 = k;
        double r1991518 = r1991516 * r1991517;
        double r1991519 = r1991513 - r1991518;
        return r1991519;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r1991520 = t;
        double r1991521 = -5.442676120004847e-262;
        bool r1991522 = r1991520 <= r1991521;
        double r1991523 = b;
        double r1991524 = c;
        double r1991525 = r1991523 * r1991524;
        double r1991526 = 18.0;
        double r1991527 = r1991526 * r1991520;
        double r1991528 = y;
        double r1991529 = z;
        double r1991530 = r1991528 * r1991529;
        double r1991531 = x;
        double r1991532 = r1991530 * r1991531;
        double r1991533 = r1991527 * r1991532;
        double r1991534 = 4.0;
        double r1991535 = a;
        double r1991536 = r1991535 * r1991520;
        double r1991537 = r1991534 * r1991536;
        double r1991538 = r1991533 - r1991537;
        double r1991539 = r1991525 + r1991538;
        double r1991540 = r1991531 * r1991534;
        double r1991541 = i;
        double r1991542 = r1991540 * r1991541;
        double r1991543 = r1991539 - r1991542;
        double r1991544 = j;
        double r1991545 = 27.0;
        double r1991546 = k;
        double r1991547 = r1991545 * r1991546;
        double r1991548 = r1991544 * r1991547;
        double r1991549 = r1991543 - r1991548;
        double r1991550 = 7.540536889545399e-05;
        bool r1991551 = r1991520 <= r1991550;
        double r1991552 = r1991520 * r1991529;
        double r1991553 = r1991526 * r1991531;
        double r1991554 = r1991553 * r1991528;
        double r1991555 = r1991552 * r1991554;
        double r1991556 = r1991534 * r1991535;
        double r1991557 = r1991556 * r1991520;
        double r1991558 = r1991555 - r1991557;
        double r1991559 = r1991525 + r1991558;
        double r1991560 = r1991559 - r1991542;
        double r1991561 = r1991544 * r1991545;
        double r1991562 = r1991546 * r1991561;
        double r1991563 = r1991560 - r1991562;
        double r1991564 = r1991551 ? r1991563 : r1991549;
        double r1991565 = r1991522 ? r1991549 : r1991564;
        return r1991565;
}

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 t < -5.442676120004847e-262 or 7.540536889545399e-05 < t

    1. Initial program 3.6

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

    2. Taylor expanded around inf 4.2

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

    3. Taylor expanded around 0 4.2

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

    5. Applied associate-*l*4.2

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

    7. Applied associate-*r*4.3

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

    if -5.442676120004847e-262 < t < 7.540536889545399e-05

    1. Initial program 7.4

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

    3. Applied associate-*l*3.8

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.442676120004847 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) - 4.0 \cdot \left(a \cdot t\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;t \le 7.540536889545399 \cdot 10^{-05}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(\left(18.0 \cdot x\right) \cdot y\right) - \left(4.0 \cdot a\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - k \cdot \left(j \cdot 27.0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18.0 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) - 4.0 \cdot \left(a \cdot t\right)\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(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)))