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

Average Error: 5.5 → 1.3

Time: 46.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -1.2815351477786883 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 1.1463779935146862 \cdot 10^{+289}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \sqrt[3]{k} \cdot \left(\left(j \cdot 27.0\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r4617289 = x;
        double r4617290 = 18.0;
        double r4617291 = r4617289 * r4617290;
        double r4617292 = y;
        double r4617293 = r4617291 * r4617292;
        double r4617294 = z;
        double r4617295 = r4617293 * r4617294;
        double r4617296 = t;
        double r4617297 = r4617295 * r4617296;
        double r4617298 = a;
        double r4617299 = 4.0;
        double r4617300 = r4617298 * r4617299;
        double r4617301 = r4617300 * r4617296;
        double r4617302 = r4617297 - r4617301;
        double r4617303 = b;
        double r4617304 = c;
        double r4617305 = r4617303 * r4617304;
        double r4617306 = r4617302 + r4617305;
        double r4617307 = r4617289 * r4617299;
        double r4617308 = i;
        double r4617309 = r4617307 * r4617308;
        double r4617310 = r4617306 - r4617309;
        double r4617311 = j;
        double r4617312 = 27.0;
        double r4617313 = r4617311 * r4617312;
        double r4617314 = k;
        double r4617315 = r4617313 * r4617314;
        double r4617316 = r4617310 - r4617315;
        return r4617316;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r4617317 = t;
        double r4617318 = x;
        double r4617319 = 18.0;
        double r4617320 = r4617318 * r4617319;
        double r4617321 = y;
        double r4617322 = r4617320 * r4617321;
        double r4617323 = z;
        double r4617324 = r4617322 * r4617323;
        double r4617325 = r4617317 * r4617324;
        double r4617326 = a;
        double r4617327 = 4.0;
        double r4617328 = r4617326 * r4617327;
        double r4617329 = r4617328 * r4617317;
        double r4617330 = r4617325 - r4617329;
        double r4617331 = c;
        double r4617332 = b;
        double r4617333 = r4617331 * r4617332;
        double r4617334 = r4617330 + r4617333;
        double r4617335 = r4617318 * r4617327;
        double r4617336 = i;
        double r4617337 = r4617335 * r4617336;
        double r4617338 = r4617334 - r4617337;
        double r4617339 = -1.2815351477786883e+306;
        bool r4617340 = r4617338 <= r4617339;
        double r4617341 = r4617317 * r4617323;
        double r4617342 = r4617341 * r4617321;
        double r4617343 = r4617342 * r4617320;
        double r4617344 = r4617343 - r4617329;
        double r4617345 = r4617333 + r4617344;
        double r4617346 = r4617345 - r4617337;
        double r4617347 = j;
        double r4617348 = 27.0;
        double r4617349 = k;
        double r4617350 = r4617348 * r4617349;
        double r4617351 = r4617347 * r4617350;
        double r4617352 = r4617346 - r4617351;
        double r4617353 = 1.1463779935146862e+289;
        bool r4617354 = r4617338 <= r4617353;
        double r4617355 = cbrt(r4617349);
        double r4617356 = r4617347 * r4617348;
        double r4617357 = r4617355 * r4617355;
        double r4617358 = r4617356 * r4617357;
        double r4617359 = r4617355 * r4617358;
        double r4617360 = r4617338 - r4617359;
        double r4617361 = r4617354 ? r4617360 : r4617352;
        double r4617362 = r4617340 ? r4617352 : r4617361;
        return r4617362;
}

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 2 regimes

2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -1.2815351477786883e+306 or 1.1463779935146862e+289 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

   1. Initial program 44.1

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

   3. Applied associate-*l* 43.9

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

   5. Applied associate-*l* 26.6

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

   7. Applied associate-*l* 6.5

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

   if -1.2815351477786883e+306 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 1.1463779935146862e+289

   1. Initial program 0.4

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

   3. Applied add-cube-cbrt 0.6

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot \color{blue}{\left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \sqrt[3]{k}\right)}\]

   4. Applied associate-*r* 0.7

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -1.2815351477786883 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 1.1463779935146862 \cdot 10^{+289}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \sqrt[3]{k} \cdot \left(\left(j \cdot 27.0\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 
(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)))