Average Error: 5.6 → 1.9
Time: 38.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6877626944398136512086016:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \le 56517438608387023208118747136:\\ \;\;\;\;\left(\left(\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array}\]
\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 -6877626944398136512086016:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\

\mathbf{elif}\;t \le 56517438608387023208118747136:\\
\;\;\;\;\left(\left(\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot j\right) \cdot k\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\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 r6324107 = x;
        double r6324108 = 18.0;
        double r6324109 = r6324107 * r6324108;
        double r6324110 = y;
        double r6324111 = r6324109 * r6324110;
        double r6324112 = z;
        double r6324113 = r6324111 * r6324112;
        double r6324114 = t;
        double r6324115 = r6324113 * r6324114;
        double r6324116 = a;
        double r6324117 = 4.0;
        double r6324118 = r6324116 * r6324117;
        double r6324119 = r6324118 * r6324114;
        double r6324120 = r6324115 - r6324119;
        double r6324121 = b;
        double r6324122 = c;
        double r6324123 = r6324121 * r6324122;
        double r6324124 = r6324120 + r6324123;
        double r6324125 = r6324107 * r6324117;
        double r6324126 = i;
        double r6324127 = r6324125 * r6324126;
        double r6324128 = r6324124 - r6324127;
        double r6324129 = j;
        double r6324130 = 27.0;
        double r6324131 = r6324129 * r6324130;
        double r6324132 = k;
        double r6324133 = r6324131 * r6324132;
        double r6324134 = r6324128 - r6324133;
        return r6324134;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r6324135 = t;
        double r6324136 = -6.877626944398137e+24;
        bool r6324137 = r6324135 <= r6324136;
        double r6324138 = b;
        double r6324139 = c;
        double r6324140 = r6324138 * r6324139;
        double r6324141 = z;
        double r6324142 = y;
        double r6324143 = x;
        double r6324144 = r6324142 * r6324143;
        double r6324145 = 18.0;
        double r6324146 = r6324144 * r6324145;
        double r6324147 = r6324141 * r6324146;
        double r6324148 = r6324147 * r6324135;
        double r6324149 = a;
        double r6324150 = 4.0;
        double r6324151 = r6324149 * r6324150;
        double r6324152 = r6324135 * r6324151;
        double r6324153 = r6324148 - r6324152;
        double r6324154 = r6324140 + r6324153;
        double r6324155 = r6324143 * r6324150;
        double r6324156 = i;
        double r6324157 = r6324155 * r6324156;
        double r6324158 = r6324154 - r6324157;
        double r6324159 = 27.0;
        double r6324160 = k;
        double r6324161 = j;
        double r6324162 = r6324160 * r6324161;
        double r6324163 = r6324159 * r6324162;
        double r6324164 = r6324158 - r6324163;
        double r6324165 = 5.651743860838702e+28;
        bool r6324166 = r6324135 <= r6324165;
        double r6324167 = r6324135 * r6324141;
        double r6324168 = r6324142 * r6324167;
        double r6324169 = r6324143 * r6324145;
        double r6324170 = r6324168 * r6324169;
        double r6324171 = r6324170 - r6324152;
        double r6324172 = r6324171 + r6324140;
        double r6324173 = r6324172 - r6324157;
        double r6324174 = r6324159 * r6324161;
        double r6324175 = r6324174 * r6324160;
        double r6324176 = r6324173 - r6324175;
        double r6324177 = r6324166 ? r6324176 : r6324164;
        double r6324178 = r6324137 ? r6324164 : r6324177;
        return r6324178;
}

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 < -6.877626944398137e+24 or 5.651743860838702e+28 < t

    1. Initial program 1.7

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

    2. Taylor expanded around 0 1.7

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

    3. Taylor expanded around 0 1.7

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

    if -6.877626944398137e+24 < t < 5.651743860838702e+28

    1. Initial program 7.5

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

    3. Applied associate-*l*4.2

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

    5. Applied associate-*l*2.0

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6877626944398136512086016:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \le 56517438608387023208118747136:\\ \;\;\;\;\left(\left(\left(\left(y \cdot \left(t \cdot z\right)\right) \cdot \left(x \cdot 18\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot j\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot t - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))