Average Error: 5.7 → 1.9
Time: 59.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.195155711809155807680860061394112481281 \cdot 10^{-8} \lor \neg \left(t \le 2.31151223505437160335095837777905012401 \cdot 10^{-51}\right):\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(\left(-t\right) + t\right) \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]
\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 -2.195155711809155807680860061394112481281 \cdot 10^{-8} \lor \neg \left(t \le 2.31151223505437160335095837777905012401 \cdot 10^{-51}\right):\\
\;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(\left(-t\right) + t\right) \cdot \left(a \cdot 4\right)\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(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\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\\

\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 r133142 = x;
        double r133143 = 18.0;
        double r133144 = r133142 * r133143;
        double r133145 = y;
        double r133146 = r133144 * r133145;
        double r133147 = z;
        double r133148 = r133146 * r133147;
        double r133149 = t;
        double r133150 = r133148 * r133149;
        double r133151 = a;
        double r133152 = 4.0;
        double r133153 = r133151 * r133152;
        double r133154 = r133153 * r133149;
        double r133155 = r133150 - r133154;
        double r133156 = b;
        double r133157 = c;
        double r133158 = r133156 * r133157;
        double r133159 = r133155 + r133158;
        double r133160 = r133142 * r133152;
        double r133161 = i;
        double r133162 = r133160 * r133161;
        double r133163 = r133159 - r133162;
        double r133164 = j;
        double r133165 = 27.0;
        double r133166 = r133164 * r133165;
        double r133167 = k;
        double r133168 = r133166 * r133167;
        double r133169 = r133163 - r133168;
        return r133169;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r133170 = t;
        double r133171 = -2.1951557118091558e-08;
        bool r133172 = r133170 <= r133171;
        double r133173 = 2.3115122350543716e-51;
        bool r133174 = r133170 <= r133173;
        double r133175 = !r133174;
        bool r133176 = r133172 || r133175;
        double r133177 = x;
        double r133178 = 18.0;
        double r133179 = r133177 * r133178;
        double r133180 = y;
        double r133181 = r133179 * r133180;
        double r133182 = z;
        double r133183 = r133181 * r133182;
        double r133184 = a;
        double r133185 = 4.0;
        double r133186 = r133184 * r133185;
        double r133187 = r133183 - r133186;
        double r133188 = r133170 * r133187;
        double r133189 = -r133170;
        double r133190 = r133189 + r133170;
        double r133191 = r133190 * r133186;
        double r133192 = r133188 + r133191;
        double r133193 = b;
        double r133194 = c;
        double r133195 = r133193 * r133194;
        double r133196 = r133192 + r133195;
        double r133197 = r133177 * r133185;
        double r133198 = i;
        double r133199 = r133197 * r133198;
        double r133200 = r133196 - r133199;
        double r133201 = j;
        double r133202 = 27.0;
        double r133203 = k;
        double r133204 = r133202 * r133203;
        double r133205 = r133201 * r133204;
        double r133206 = r133200 - r133205;
        double r133207 = r133182 * r133170;
        double r133208 = r133180 * r133207;
        double r133209 = r133179 * r133208;
        double r133210 = r133186 * r133170;
        double r133211 = r133209 - r133210;
        double r133212 = r133211 + r133195;
        double r133213 = r133212 - r133199;
        double r133214 = r133201 * r133202;
        double r133215 = r133214 * r133203;
        double r133216 = r133213 - r133215;
        double r133217 = r133176 ? r133206 : r133216;
        return r133217;
}

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 t < -2.1951557118091558e-08 or 2.3115122350543716e-51 < t

    1. Initial program 2.2

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

    3. Applied associate-*l*9.1

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

    5. Applied prod-diff9.1

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

    6. Simplified2.2

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

    7. Simplified2.2

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

    9. Applied associate-*l*2.2

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

    if -2.1951557118091558e-08 < t < 2.3115122350543716e-51

    1. Initial program 8.3

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

    3. Applied associate-*l*4.8

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

    5. Applied associate-*l*1.6

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.195155711809155807680860061394112481281 \cdot 10^{-8} \lor \neg \left(t \le 2.31151223505437160335095837777905012401 \cdot 10^{-51}\right):\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(\left(-t\right) + t\right) \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +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)))