Average Error: 5.5 → 3.9
Time: 30.9s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.817835946533626758757686769633005516507 \cdot 10^{-98}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;y \le 1.919804578831060539244494100787191703918 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;y \le -4.817835946533626758757686769633005516507 \cdot 10^{-98}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\

\mathbf{elif}\;y \le 1.919804578831060539244494100787191703918 \cdot 10^{-79}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\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 r7547502 = x;
        double r7547503 = 18.0;
        double r7547504 = r7547502 * r7547503;
        double r7547505 = y;
        double r7547506 = r7547504 * r7547505;
        double r7547507 = z;
        double r7547508 = r7547506 * r7547507;
        double r7547509 = t;
        double r7547510 = r7547508 * r7547509;
        double r7547511 = a;
        double r7547512 = 4.0;
        double r7547513 = r7547511 * r7547512;
        double r7547514 = r7547513 * r7547509;
        double r7547515 = r7547510 - r7547514;
        double r7547516 = b;
        double r7547517 = c;
        double r7547518 = r7547516 * r7547517;
        double r7547519 = r7547515 + r7547518;
        double r7547520 = r7547502 * r7547512;
        double r7547521 = i;
        double r7547522 = r7547520 * r7547521;
        double r7547523 = r7547519 - r7547522;
        double r7547524 = j;
        double r7547525 = 27.0;
        double r7547526 = r7547524 * r7547525;
        double r7547527 = k;
        double r7547528 = r7547526 * r7547527;
        double r7547529 = r7547523 - r7547528;
        return r7547529;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r7547530 = y;
        double r7547531 = -4.817835946533627e-98;
        bool r7547532 = r7547530 <= r7547531;
        double r7547533 = b;
        double r7547534 = c;
        double r7547535 = r7547533 * r7547534;
        double r7547536 = t;
        double r7547537 = z;
        double r7547538 = r7547536 * r7547537;
        double r7547539 = r7547530 * r7547538;
        double r7547540 = x;
        double r7547541 = 18.0;
        double r7547542 = r7547540 * r7547541;
        double r7547543 = r7547539 * r7547542;
        double r7547544 = a;
        double r7547545 = 4.0;
        double r7547546 = r7547544 * r7547545;
        double r7547547 = r7547536 * r7547546;
        double r7547548 = r7547543 - r7547547;
        double r7547549 = r7547535 + r7547548;
        double r7547550 = r7547545 * r7547540;
        double r7547551 = i;
        double r7547552 = r7547550 * r7547551;
        double r7547553 = r7547549 - r7547552;
        double r7547554 = j;
        double r7547555 = 27.0;
        double r7547556 = k;
        double r7547557 = r7547555 * r7547556;
        double r7547558 = r7547554 * r7547557;
        double r7547559 = r7547553 - r7547558;
        double r7547560 = 1.9198045788310605e-79;
        bool r7547561 = r7547530 <= r7547560;
        double r7547562 = r7547530 * r7547537;
        double r7547563 = r7547562 * r7547536;
        double r7547564 = r7547563 * r7547542;
        double r7547565 = r7547564 - r7547547;
        double r7547566 = r7547535 + r7547565;
        double r7547567 = r7547566 - r7547552;
        double r7547568 = r7547554 * r7547556;
        double r7547569 = r7547555 * r7547568;
        double r7547570 = r7547567 - r7547569;
        double r7547571 = r7547561 ? r7547570 : r7547559;
        double r7547572 = r7547532 ? r7547559 : r7547571;
        return r7547572;
}

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 y < -4.817835946533627e-98 or 1.9198045788310605e-79 < y

    1. Initial program 8.5

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

    3. Applied associate-*l*10.5

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

    5. Applied associate-*l*10.6

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

    7. Applied associate-*l*10.6

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

    9. Applied associate-*l*6.2

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

    if -4.817835946533627e-98 < y < 1.9198045788310605e-79

    1. Initial program 0.9

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

    3. Applied associate-*l*0.7

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

    5. Applied associate-*l*0.7

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

    6. Taylor expanded around 0 0.6

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

  4. Final simplification3.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.817835946533626758757686769633005516507 \cdot 10^{-98}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;y \le 1.919804578831060539244494100787191703918 \cdot 10^{-79}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(y \cdot z\right) \cdot t\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(4 \cdot x\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))