Average Error: 5.5 → 4.0
Time: 24.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.802521353136590134090568041763149695323 \cdot 10^{-178}:\\ \;\;\;\;\left(\left(\left(\left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \le 4.339340101075432744492970777980355608709 \cdot 10^{-63}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(t \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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}\;t \le -4.802521353136590134090568041763149695323 \cdot 10^{-178}:\\
\;\;\;\;\left(\left(\left(\left(z \cdot \left(18 \cdot \left(x \cdot y\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\\

\mathbf{elif}\;t \le 4.339340101075432744492970777980355608709 \cdot 10^{-63}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(t \cdot z\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(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) - 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 r88237 = x;
        double r88238 = 18.0;
        double r88239 = r88237 * r88238;
        double r88240 = y;
        double r88241 = r88239 * r88240;
        double r88242 = z;
        double r88243 = r88241 * r88242;
        double r88244 = t;
        double r88245 = r88243 * r88244;
        double r88246 = a;
        double r88247 = 4.0;
        double r88248 = r88246 * r88247;
        double r88249 = r88248 * r88244;
        double r88250 = r88245 - r88249;
        double r88251 = b;
        double r88252 = c;
        double r88253 = r88251 * r88252;
        double r88254 = r88250 + r88253;
        double r88255 = r88237 * r88247;
        double r88256 = i;
        double r88257 = r88255 * r88256;
        double r88258 = r88254 - r88257;
        double r88259 = j;
        double r88260 = 27.0;
        double r88261 = r88259 * r88260;
        double r88262 = k;
        double r88263 = r88261 * r88262;
        double r88264 = r88258 - r88263;
        return r88264;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r88265 = t;
        double r88266 = -4.80252135313659e-178;
        bool r88267 = r88265 <= r88266;
        double r88268 = z;
        double r88269 = 18.0;
        double r88270 = x;
        double r88271 = y;
        double r88272 = r88270 * r88271;
        double r88273 = r88269 * r88272;
        double r88274 = r88268 * r88273;
        double r88275 = r88274 * r88265;
        double r88276 = a;
        double r88277 = 4.0;
        double r88278 = r88276 * r88277;
        double r88279 = r88278 * r88265;
        double r88280 = r88275 - r88279;
        double r88281 = b;
        double r88282 = c;
        double r88283 = r88281 * r88282;
        double r88284 = r88280 + r88283;
        double r88285 = r88270 * r88277;
        double r88286 = i;
        double r88287 = r88285 * r88286;
        double r88288 = r88284 - r88287;
        double r88289 = j;
        double r88290 = 27.0;
        double r88291 = r88289 * r88290;
        double r88292 = k;
        double r88293 = r88291 * r88292;
        double r88294 = r88288 - r88293;
        double r88295 = 4.339340101075433e-63;
        bool r88296 = r88265 <= r88295;
        double r88297 = r88270 * r88269;
        double r88298 = r88297 * r88271;
        double r88299 = r88265 * r88268;
        double r88300 = r88298 * r88299;
        double r88301 = r88300 - r88279;
        double r88302 = r88301 + r88283;
        double r88303 = r88302 - r88287;
        double r88304 = r88290 * r88292;
        double r88305 = r88289 * r88304;
        double r88306 = r88303 - r88305;
        double r88307 = r88271 * r88268;
        double r88308 = r88297 * r88307;
        double r88309 = r88308 * r88265;
        double r88310 = r88309 - r88279;
        double r88311 = r88310 + r88283;
        double r88312 = r88311 - r88287;
        double r88313 = r88312 - r88305;
        double r88314 = r88296 ? r88306 : r88313;
        double r88315 = r88267 ? r88294 : r88314;
        return r88315;
}

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 < -4.80252135313659e-178

    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. Using strategy rm

    3. Applied associate-*l*4.0

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

    4. Simplified4.0

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

    6. Applied *-un-lft-identity4.0

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    7. Applied associate-*r*4.0

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot 1\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    8. Simplified4.0

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

    if -4.80252135313659e-178 < t < 4.339340101075433e-63

    1. Initial program 8.5

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

    3. Applied associate-*l*8.5

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

    5. Applied associate-*l*4.5

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

    6. Simplified4.5

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

    if 4.339340101075433e-63 < t

    1. Initial program 3.0

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

    3. Applied associate-*l*3.0

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

    5. Applied associate-*l*3.3

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

  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.802521353136590134090568041763149695323 \cdot 10^{-178}:\\ \;\;\;\;\left(\left(\left(\left(z \cdot \left(18 \cdot \left(x \cdot y\right)\right)\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \le 4.339340101075432744492970777980355608709 \cdot 10^{-63}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(t \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(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)))