Average Error: 5.5 → 3.1
Time: 6.4s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 5.3319379792198453 \cdot 10^{304}\right):\\ \;\;\;\;\left(\left(\left(0 \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \left(\sqrt[3]{j \cdot 27} \cdot \sqrt[3]{k}\right)\\ \end{array}\]
\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 5.3319379792198453 \cdot 10^{304}\right):\\
\;\;\;\;\left(\left(\left(0 \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(\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(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \left(\sqrt[3]{j \cdot 27} \cdot \sqrt[3]{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 r158183 = x;
        double r158184 = 18.0;
        double r158185 = r158183 * r158184;
        double r158186 = y;
        double r158187 = r158185 * r158186;
        double r158188 = z;
        double r158189 = r158187 * r158188;
        double r158190 = t;
        double r158191 = r158189 * r158190;
        double r158192 = a;
        double r158193 = 4.0;
        double r158194 = r158192 * r158193;
        double r158195 = r158194 * r158190;
        double r158196 = r158191 - r158195;
        double r158197 = b;
        double r158198 = c;
        double r158199 = r158197 * r158198;
        double r158200 = r158196 + r158199;
        double r158201 = r158183 * r158193;
        double r158202 = i;
        double r158203 = r158201 * r158202;
        double r158204 = r158200 - r158203;
        double r158205 = j;
        double r158206 = 27.0;
        double r158207 = r158205 * r158206;
        double r158208 = k;
        double r158209 = r158207 * r158208;
        double r158210 = r158204 - r158209;
        return r158210;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r158211 = x;
        double r158212 = 18.0;
        double r158213 = r158211 * r158212;
        double r158214 = y;
        double r158215 = r158213 * r158214;
        double r158216 = z;
        double r158217 = r158215 * r158216;
        double r158218 = t;
        double r158219 = r158217 * r158218;
        double r158220 = a;
        double r158221 = 4.0;
        double r158222 = r158220 * r158221;
        double r158223 = r158222 * r158218;
        double r158224 = r158219 - r158223;
        double r158225 = b;
        double r158226 = c;
        double r158227 = r158225 * r158226;
        double r158228 = r158224 + r158227;
        double r158229 = r158211 * r158221;
        double r158230 = i;
        double r158231 = r158229 * r158230;
        double r158232 = r158228 - r158231;
        double r158233 = -inf.0;
        bool r158234 = r158232 <= r158233;
        double r158235 = 5.331937979219845e+304;
        bool r158236 = r158232 <= r158235;
        double r158237 = !r158236;
        bool r158238 = r158234 || r158237;
        double r158239 = 0.0;
        double r158240 = r158239 * r158218;
        double r158241 = r158240 - r158223;
        double r158242 = r158241 + r158227;
        double r158243 = r158242 - r158231;
        double r158244 = j;
        double r158245 = 27.0;
        double r158246 = k;
        double r158247 = r158245 * r158246;
        double r158248 = r158244 * r158247;
        double r158249 = r158243 - r158248;
        double r158250 = r158244 * r158245;
        double r158251 = r158250 * r158246;
        double r158252 = cbrt(r158251);
        double r158253 = r158252 * r158252;
        double r158254 = cbrt(r158250);
        double r158255 = cbrt(r158246);
        double r158256 = r158254 * r158255;
        double r158257 = r158253 * r158256;
        double r158258 = r158232 - r158257;
        double r158259 = r158238 ? r158249 : r158258;
        return r158259;
}

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 5.331937979219845e+304 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 60.5

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

    3. Applied associate-*l*60.5

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

    4. Taylor expanded around 0 29.9

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

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 5.331937979219845e+304

    1. Initial program 0.4

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

    3. Applied add-cube-cbrt0.6

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

    5. Applied cbrt-prod0.6

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 5.3319379792198453 \cdot 10^{304}\right):\\ \;\;\;\;\left(\left(\left(0 \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \left(\sqrt[3]{j \cdot 27} \cdot \sqrt[3]{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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)))