Average Error: 5.9 → 6.5
Time: 7.4s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;b \cdot c \le -1.19023077614854233 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]
\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}\;b \cdot c \le -1.19023077614854233 \cdot 10^{-42}:\\
\;\;\;\;t \cdot \left(0 - 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)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\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 r136161 = x;
        double r136162 = 18.0;
        double r136163 = r136161 * r136162;
        double r136164 = y;
        double r136165 = r136163 * r136164;
        double r136166 = z;
        double r136167 = r136165 * r136166;
        double r136168 = t;
        double r136169 = r136167 * r136168;
        double r136170 = a;
        double r136171 = 4.0;
        double r136172 = r136170 * r136171;
        double r136173 = r136172 * r136168;
        double r136174 = r136169 - r136173;
        double r136175 = b;
        double r136176 = c;
        double r136177 = r136175 * r136176;
        double r136178 = r136174 + r136177;
        double r136179 = r136161 * r136171;
        double r136180 = i;
        double r136181 = r136179 * r136180;
        double r136182 = r136178 - r136181;
        double r136183 = j;
        double r136184 = 27.0;
        double r136185 = r136183 * r136184;
        double r136186 = k;
        double r136187 = r136185 * r136186;
        double r136188 = r136182 - r136187;
        return r136188;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r136189 = b;
        double r136190 = c;
        double r136191 = r136189 * r136190;
        double r136192 = -1.1902307761485423e-42;
        bool r136193 = r136191 <= r136192;
        double r136194 = t;
        double r136195 = 0.0;
        double r136196 = a;
        double r136197 = 4.0;
        double r136198 = r136196 * r136197;
        double r136199 = r136195 - r136198;
        double r136200 = r136194 * r136199;
        double r136201 = x;
        double r136202 = r136201 * r136197;
        double r136203 = i;
        double r136204 = r136202 * r136203;
        double r136205 = j;
        double r136206 = 27.0;
        double r136207 = k;
        double r136208 = r136206 * r136207;
        double r136209 = r136205 * r136208;
        double r136210 = r136204 + r136209;
        double r136211 = r136191 - r136210;
        double r136212 = r136200 + r136211;
        double r136213 = 18.0;
        double r136214 = r136201 * r136213;
        double r136215 = y;
        double r136216 = r136214 * r136215;
        double r136217 = cbrt(r136216);
        double r136218 = r136217 * r136217;
        double r136219 = r136218 * r136217;
        double r136220 = z;
        double r136221 = r136219 * r136220;
        double r136222 = r136221 - r136198;
        double r136223 = r136194 * r136222;
        double r136224 = r136223 + r136211;
        double r136225 = r136193 ? r136212 : r136224;
        return r136225;
}

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 (* b c) < -1.1902307761485423e-42

    1. Initial program 5.1

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

    2. Simplified5.1

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

    4. Applied associate-*l*5.2

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

    5. Taylor expanded around 0 7.5

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

    if -1.1902307761485423e-42 < (* b c)

    1. Initial program 6.1

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

    2. Simplified6.1

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

    4. Applied associate-*l*6.1

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

    6. Applied add-cube-cbrt6.2

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

  4. Final simplification6.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \le -1.19023077614854233 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020059 
(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)))