Average Error: 5.9 → 1.8
Time: 7.9s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 1.408347514255849598590216064760682864053 \cdot 10^{307}\right):\\ \;\;\;\;\left(\left(\left(x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;\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 = -\infty \lor \neg \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 \le 1.408347514255849598590216064760682864053 \cdot 10^{307}\right):\\
\;\;\;\;\left(\left(\left(x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\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)\\

\mathbf{else}:\\
\;\;\;\;\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)\\

\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 r173247 = x;
        double r173248 = 18.0;
        double r173249 = r173247 * r173248;
        double r173250 = y;
        double r173251 = r173249 * r173250;
        double r173252 = z;
        double r173253 = r173251 * r173252;
        double r173254 = t;
        double r173255 = r173253 * r173254;
        double r173256 = a;
        double r173257 = 4.0;
        double r173258 = r173256 * r173257;
        double r173259 = r173258 * r173254;
        double r173260 = r173255 - r173259;
        double r173261 = b;
        double r173262 = c;
        double r173263 = r173261 * r173262;
        double r173264 = r173260 + r173263;
        double r173265 = r173247 * r173257;
        double r173266 = i;
        double r173267 = r173265 * r173266;
        double r173268 = r173264 - r173267;
        double r173269 = j;
        double r173270 = 27.0;
        double r173271 = r173269 * r173270;
        double r173272 = k;
        double r173273 = r173271 * r173272;
        double r173274 = r173268 - r173273;
        return r173274;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r173275 = x;
        double r173276 = 18.0;
        double r173277 = r173275 * r173276;
        double r173278 = y;
        double r173279 = r173277 * r173278;
        double r173280 = z;
        double r173281 = r173279 * r173280;
        double r173282 = t;
        double r173283 = r173281 * r173282;
        double r173284 = a;
        double r173285 = 4.0;
        double r173286 = r173284 * r173285;
        double r173287 = r173286 * r173282;
        double r173288 = r173283 - r173287;
        double r173289 = b;
        double r173290 = c;
        double r173291 = r173289 * r173290;
        double r173292 = r173288 + r173291;
        double r173293 = r173275 * r173285;
        double r173294 = i;
        double r173295 = r173293 * r173294;
        double r173296 = r173292 - r173295;
        double r173297 = -inf.0;
        bool r173298 = r173296 <= r173297;
        double r173299 = 1.4083475142558496e+307;
        bool r173300 = r173296 <= r173299;
        double r173301 = !r173300;
        bool r173302 = r173298 || r173301;
        double r173303 = r173278 * r173280;
        double r173304 = r173276 * r173303;
        double r173305 = r173304 * r173282;
        double r173306 = r173275 * r173305;
        double r173307 = r173306 - r173287;
        double r173308 = r173307 + r173291;
        double r173309 = r173308 - r173295;
        double r173310 = j;
        double r173311 = 27.0;
        double r173312 = k;
        double r173313 = r173311 * r173312;
        double r173314 = r173310 * r173313;
        double r173315 = r173309 - r173314;
        double r173316 = r173296 - r173314;
        double r173317 = r173302 ? r173315 : r173316;
        return r173317;
}

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 (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0 or 1.4083475142558496e+307 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 63.0

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

    3. Applied associate-*l*40.5

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

    5. Applied associate-*l*40.2

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

    7. Applied associate-*l*40.3

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

    9. Applied associate-*l*16.8

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

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 1.4083475142558496e+307

    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*0.3

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 1.408347514255849598590216064760682864053 \cdot 10^{307}\right):\\ \;\;\;\;\left(\left(\left(x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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)))