Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

Average Error: 5.5 → 1.6

Time: 7.5s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le -2.03888388659653177 \cdot 10^{295}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 2.661920863197471 \cdot 10^{300}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r133662 = x;
        double r133663 = 18.0;
        double r133664 = r133662 * r133663;
        double r133665 = y;
        double r133666 = r133664 * r133665;
        double r133667 = z;
        double r133668 = r133666 * r133667;
        double r133669 = t;
        double r133670 = r133668 * r133669;
        double r133671 = a;
        double r133672 = 4.0;
        double r133673 = r133671 * r133672;
        double r133674 = r133673 * r133669;
        double r133675 = r133670 - r133674;
        double r133676 = b;
        double r133677 = c;
        double r133678 = r133676 * r133677;
        double r133679 = r133675 + r133678;
        double r133680 = r133662 * r133672;
        double r133681 = i;
        double r133682 = r133680 * r133681;
        double r133683 = r133679 - r133682;
        double r133684 = j;
        double r133685 = 27.0;
        double r133686 = r133684 * r133685;
        double r133687 = k;
        double r133688 = r133686 * r133687;
        double r133689 = r133683 - r133688;
        return r133689;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r133690 = x;
        double r133691 = 18.0;
        double r133692 = r133690 * r133691;
        double r133693 = y;
        double r133694 = r133692 * r133693;
        double r133695 = z;
        double r133696 = r133694 * r133695;
        double r133697 = t;
        double r133698 = r133696 * r133697;
        double r133699 = a;
        double r133700 = 4.0;
        double r133701 = r133699 * r133700;
        double r133702 = r133701 * r133697;
        double r133703 = r133698 - r133702;
        double r133704 = b;
        double r133705 = c;
        double r133706 = r133704 * r133705;
        double r133707 = r133703 + r133706;
        double r133708 = r133690 * r133700;
        double r133709 = i;
        double r133710 = r133708 * r133709;
        double r133711 = r133707 - r133710;
        double r133712 = -2.0388838865965318e+295;
        bool r133713 = r133711 <= r133712;
        double r133714 = r133695 * r133697;
        double r133715 = r133693 * r133714;
        double r133716 = r133692 * r133715;
        double r133717 = r133716 - r133702;
        double r133718 = r133717 + r133706;
        double r133719 = r133718 - r133710;
        double r133720 = j;
        double r133721 = 27.0;
        double r133722 = r133720 * r133721;
        double r133723 = k;
        double r133724 = r133722 * r133723;
        double r133725 = r133719 - r133724;
        double r133726 = 2.661920863197471e+300;
        bool r133727 = r133711 <= r133726;
        double r133728 = r133721 * r133723;
        double r133729 = r133720 * r133728;
        double r133730 = r133711 - r133729;
        double r133731 = r133693 * r133695;
        double r133732 = r133731 * r133697;
        double r133733 = r133692 * r133732;
        double r133734 = r133733 - r133702;
        double r133735 = r133734 + r133706;
        double r133736 = r133735 - r133710;
        double r133737 = r133736 - r133724;
        double r133738 = r133727 ? r133730 : r133737;
        double r133739 = r133713 ? r133725 : r133738;
        return r133739;
}

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

Derivation

1. Split input into 3 regimes

2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -2.0388838865965318e+295

   1. Initial program 44.3

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

   3. Applied associate-*l* 28.1

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

   5. Applied associate-*l* 16.2

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

   7. Applied associate-*l* 7.9

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

   if -2.0388838865965318e+295 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 2.661920863197471e+300

   1. Initial program 0.3

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

   3. Applied associate-*l* 0.4

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

   if 2.661920863197471e+300 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

   1. Initial program 51.2

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

   3. Applied associate-*l* 33.3

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

   5. Applied associate-*l* 15.0

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

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le -2.03888388659653177 \cdot 10^{295}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 2.661920863197471 \cdot 10^{300}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(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)))