Average Error: 5.7 → 4.9
Time: 8.3s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.3782938552808126543647984854596196655 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{elif}\;t \le 1.541728241483554882113848793697671960573 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]
\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}\;t \le -8.3782938552808126543647984854596196655 \cdot 10^{-183}:\\
\;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\

\mathbf{elif}\;t \le 1.541728241483554882113848793697671960573 \cdot 10^{-174}:\\
\;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\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 r112253 = x;
        double r112254 = 18.0;
        double r112255 = r112253 * r112254;
        double r112256 = y;
        double r112257 = r112255 * r112256;
        double r112258 = z;
        double r112259 = r112257 * r112258;
        double r112260 = t;
        double r112261 = r112259 * r112260;
        double r112262 = a;
        double r112263 = 4.0;
        double r112264 = r112262 * r112263;
        double r112265 = r112264 * r112260;
        double r112266 = r112261 - r112265;
        double r112267 = b;
        double r112268 = c;
        double r112269 = r112267 * r112268;
        double r112270 = r112266 + r112269;
        double r112271 = r112253 * r112263;
        double r112272 = i;
        double r112273 = r112271 * r112272;
        double r112274 = r112270 - r112273;
        double r112275 = j;
        double r112276 = 27.0;
        double r112277 = r112275 * r112276;
        double r112278 = k;
        double r112279 = r112277 * r112278;
        double r112280 = r112274 - r112279;
        return r112280;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r112281 = t;
        double r112282 = -8.378293855280813e-183;
        bool r112283 = r112281 <= r112282;
        double r112284 = x;
        double r112285 = 18.0;
        double r112286 = r112284 * r112285;
        double r112287 = y;
        double r112288 = z;
        double r112289 = r112287 * r112288;
        double r112290 = r112286 * r112289;
        double r112291 = a;
        double r112292 = 4.0;
        double r112293 = r112291 * r112292;
        double r112294 = r112290 - r112293;
        double r112295 = r112281 * r112294;
        double r112296 = b;
        double r112297 = c;
        double r112298 = r112296 * r112297;
        double r112299 = r112284 * r112292;
        double r112300 = i;
        double r112301 = r112299 * r112300;
        double r112302 = j;
        double r112303 = 27.0;
        double r112304 = r112302 * r112303;
        double r112305 = k;
        double r112306 = r112304 * r112305;
        double r112307 = r112301 + r112306;
        double r112308 = r112298 - r112307;
        double r112309 = r112295 + r112308;
        double r112310 = 1.5417282414835549e-174;
        bool r112311 = r112281 <= r112310;
        double r112312 = 0.0;
        double r112313 = r112312 - r112293;
        double r112314 = r112281 * r112313;
        double r112315 = cbrt(r112305);
        double r112316 = r112315 * r112315;
        double r112317 = r112304 * r112316;
        double r112318 = r112317 * r112315;
        double r112319 = r112301 + r112318;
        double r112320 = r112298 - r112319;
        double r112321 = r112314 + r112320;
        double r112322 = r112286 * r112287;
        double r112323 = r112322 * r112288;
        double r112324 = r112323 - r112293;
        double r112325 = r112281 * r112324;
        double r112326 = r112303 * r112305;
        double r112327 = r112302 * r112326;
        double r112328 = r112301 + r112327;
        double r112329 = r112298 - r112328;
        double r112330 = r112325 + r112329;
        double r112331 = r112311 ? r112321 : r112330;
        double r112332 = r112283 ? r112309 : r112331;
        return r112332;
}

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 3 regimes

  2. if t < -8.378293855280813e-183

    1. Initial program 4.3

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

    2. Simplified4.3

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

    4. Applied associate-*l*4.8

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

    if -8.378293855280813e-183 < t < 1.5417282414835549e-174

    1. Initial program 9.7

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

    2. Simplified9.7

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

    4. Applied add-cube-cbrt10.0

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

    5. Applied associate-*r*10.0

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

    6. Taylor expanded around 0 6.2

      \[\leadsto t \cdot \left(\color{blue}{0} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\]

    if 1.5417282414835549e-174 < t

    1. Initial program 4.0

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

    2. Simplified4.0

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

    4. Applied associate-*l*4.0

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

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.3782938552808126543647984854596196655 \cdot 10^{-183}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{elif}\;t \le 1.541728241483554882113848793697671960573 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\left(j \cdot 27\right) \cdot \left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)\right) \cdot \sqrt[3]{k}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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)))