Average Error: 5.0 → 4.1
Time: 36.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.442676120004847 \cdot 10^{-262}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(t \cdot \left(\left(z \cdot y\right) \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;t \le 7.540536889545399 \cdot 10^{-05}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(\left(18.0 \cdot x\right) \cdot y\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(t \cdot \left(\left(z \cdot y\right) \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]
\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(18.0 \cdot \left(t \cdot \left(\left(z \cdot y\right) \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\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(z \cdot t\right) \cdot \left(\left(18.0 \cdot x\right) \cdot y\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(18.0 \cdot \left(t \cdot \left(\left(z \cdot y\right) \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\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 r2808622 = x;
        double r2808623 = 18.0;
        double r2808624 = r2808622 * r2808623;
        double r2808625 = y;
        double r2808626 = r2808624 * r2808625;
        double r2808627 = z;
        double r2808628 = r2808626 * r2808627;
        double r2808629 = t;
        double r2808630 = r2808628 * r2808629;
        double r2808631 = a;
        double r2808632 = 4.0;
        double r2808633 = r2808631 * r2808632;
        double r2808634 = r2808633 * r2808629;
        double r2808635 = r2808630 - r2808634;
        double r2808636 = b;
        double r2808637 = c;
        double r2808638 = r2808636 * r2808637;
        double r2808639 = r2808635 + r2808638;
        double r2808640 = r2808622 * r2808632;
        double r2808641 = i;
        double r2808642 = r2808640 * r2808641;
        double r2808643 = r2808639 - r2808642;
        double r2808644 = j;
        double r2808645 = 27.0;
        double r2808646 = r2808644 * r2808645;
        double r2808647 = k;
        double r2808648 = r2808646 * r2808647;
        double r2808649 = r2808643 - r2808648;
        return r2808649;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r2808650 = t;
        double r2808651 = -5.442676120004847e-262;
        bool r2808652 = r2808650 <= r2808651;
        double r2808653 = b;
        double r2808654 = c;
        double r2808655 = r2808653 * r2808654;
        double r2808656 = 18.0;
        double r2808657 = z;
        double r2808658 = y;
        double r2808659 = r2808657 * r2808658;
        double r2808660 = x;
        double r2808661 = r2808659 * r2808660;
        double r2808662 = r2808650 * r2808661;
        double r2808663 = r2808656 * r2808662;
        double r2808664 = a;
        double r2808665 = 4.0;
        double r2808666 = r2808664 * r2808665;
        double r2808667 = r2808666 * r2808650;
        double r2808668 = r2808663 - r2808667;
        double r2808669 = r2808655 + r2808668;
        double r2808670 = r2808660 * r2808665;
        double r2808671 = i;
        double r2808672 = r2808670 * r2808671;
        double r2808673 = r2808669 - r2808672;
        double r2808674 = j;
        double r2808675 = 27.0;
        double r2808676 = k;
        double r2808677 = r2808675 * r2808676;
        double r2808678 = r2808674 * r2808677;
        double r2808679 = r2808673 - r2808678;
        double r2808680 = 7.540536889545399e-05;
        bool r2808681 = r2808650 <= r2808680;
        double r2808682 = r2808657 * r2808650;
        double r2808683 = r2808656 * r2808660;
        double r2808684 = r2808683 * r2808658;
        double r2808685 = r2808682 * r2808684;
        double r2808686 = r2808685 - r2808667;
        double r2808687 = r2808655 + r2808686;
        double r2808688 = r2808687 - r2808672;
        double r2808689 = r2808674 * r2808675;
        double r2808690 = r2808689 * r2808676;
        double r2808691 = r2808688 - r2808690;
        double r2808692 = r2808681 ? r2808691 : r2808679;
        double r2808693 = r2808652 ? r2808679 : r2808692;
        return r2808693;
}

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. Using strategy rm

    4. Applied associate-*l*4.2

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

    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

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

Reproduce

herbie shell --seed 2019153 +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)))