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

Average Error: 5.5 → 1.6

Time: 10.2s

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 r207378 = x;
        double r207379 = 18.0;
        double r207380 = r207378 * r207379;
        double r207381 = y;
        double r207382 = r207380 * r207381;
        double r207383 = z;
        double r207384 = r207382 * r207383;
        double r207385 = t;
        double r207386 = r207384 * r207385;
        double r207387 = a;
        double r207388 = 4.0;
        double r207389 = r207387 * r207388;
        double r207390 = r207389 * r207385;
        double r207391 = r207386 - r207390;
        double r207392 = b;
        double r207393 = c;
        double r207394 = r207392 * r207393;
        double r207395 = r207391 + r207394;
        double r207396 = r207378 * r207388;
        double r207397 = i;
        double r207398 = r207396 * r207397;
        double r207399 = r207395 - r207398;
        double r207400 = j;
        double r207401 = 27.0;
        double r207402 = r207400 * r207401;
        double r207403 = k;
        double r207404 = r207402 * r207403;
        double r207405 = r207399 - r207404;
        return r207405;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r207406 = x;
        double r207407 = 18.0;
        double r207408 = r207406 * r207407;
        double r207409 = y;
        double r207410 = r207408 * r207409;
        double r207411 = z;
        double r207412 = r207410 * r207411;
        double r207413 = t;
        double r207414 = r207412 * r207413;
        double r207415 = a;
        double r207416 = 4.0;
        double r207417 = r207415 * r207416;
        double r207418 = r207417 * r207413;
        double r207419 = r207414 - r207418;
        double r207420 = b;
        double r207421 = c;
        double r207422 = r207420 * r207421;
        double r207423 = r207419 + r207422;
        double r207424 = r207406 * r207416;
        double r207425 = i;
        double r207426 = r207424 * r207425;
        double r207427 = r207423 - r207426;
        double r207428 = -2.0388838865965318e+295;
        bool r207429 = r207427 <= r207428;
        double r207430 = r207411 * r207413;
        double r207431 = r207409 * r207430;
        double r207432 = r207408 * r207431;
        double r207433 = r207432 - r207418;
        double r207434 = r207433 + r207422;
        double r207435 = r207434 - r207426;
        double r207436 = j;
        double r207437 = 27.0;
        double r207438 = r207436 * r207437;
        double r207439 = k;
        double r207440 = r207438 * r207439;
        double r207441 = r207435 - r207440;
        double r207442 = 2.661920863197471e+300;
        bool r207443 = r207427 <= r207442;
        double r207444 = r207437 * r207439;
        double r207445 = r207436 * r207444;
        double r207446 = r207427 - r207445;
        double r207447 = r207409 * r207411;
        double r207448 = r207447 * r207413;
        double r207449 = r207408 * r207448;
        double r207450 = r207449 - r207418;
        double r207451 = r207450 + r207422;
        double r207452 = r207451 - r207426;
        double r207453 = r207452 - r207440;
        double r207454 = r207443 ? r207446 : r207453;
        double r207455 = r207429 ? r207441 : r207454;
        return r207455;
}

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)))