Average Error: 5.8 → 4.1
Time: 24.0s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.24424295411286357321282707929428675159 \cdot 10^{-146} \lor \neg \left(z \le 128162218108037256959754240\right):\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \end{array}\]
\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}\;z \le -3.24424295411286357321282707929428675159 \cdot 10^{-146} \lor \neg \left(z \le 128162218108037256959754240\right):\\
\;\;\;\;\left(t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\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 r106092 = x;
        double r106093 = 18.0;
        double r106094 = r106092 * r106093;
        double r106095 = y;
        double r106096 = r106094 * r106095;
        double r106097 = z;
        double r106098 = r106096 * r106097;
        double r106099 = t;
        double r106100 = r106098 * r106099;
        double r106101 = a;
        double r106102 = 4.0;
        double r106103 = r106101 * r106102;
        double r106104 = r106103 * r106099;
        double r106105 = r106100 - r106104;
        double r106106 = b;
        double r106107 = c;
        double r106108 = r106106 * r106107;
        double r106109 = r106105 + r106108;
        double r106110 = r106092 * r106102;
        double r106111 = i;
        double r106112 = r106110 * r106111;
        double r106113 = r106109 - r106112;
        double r106114 = j;
        double r106115 = 27.0;
        double r106116 = r106114 * r106115;
        double r106117 = k;
        double r106118 = r106116 * r106117;
        double r106119 = r106113 - r106118;
        return r106119;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r106120 = z;
        double r106121 = -3.2442429541128636e-146;
        bool r106122 = r106120 <= r106121;
        double r106123 = 1.2816221810803726e+26;
        bool r106124 = r106120 <= r106123;
        double r106125 = !r106124;
        bool r106126 = r106122 || r106125;
        double r106127 = t;
        double r106128 = x;
        double r106129 = 18.0;
        double r106130 = y;
        double r106131 = r106129 * r106130;
        double r106132 = r106128 * r106131;
        double r106133 = r106132 * r106120;
        double r106134 = a;
        double r106135 = 4.0;
        double r106136 = r106134 * r106135;
        double r106137 = r106133 - r106136;
        double r106138 = r106127 * r106137;
        double r106139 = b;
        double r106140 = c;
        double r106141 = r106139 * r106140;
        double r106142 = r106138 + r106141;
        double r106143 = r106128 * r106135;
        double r106144 = i;
        double r106145 = r106143 * r106144;
        double r106146 = j;
        double r106147 = 27.0;
        double r106148 = k;
        double r106149 = r106147 * r106148;
        double r106150 = r106146 * r106149;
        double r106151 = r106145 + r106150;
        double r106152 = r106142 - r106151;
        double r106153 = r106128 * r106129;
        double r106154 = r106120 * r106130;
        double r106155 = r106153 * r106154;
        double r106156 = r106155 - r106136;
        double r106157 = r106127 * r106156;
        double r106158 = r106157 + r106141;
        double r106159 = r106158 - r106151;
        double r106160 = r106126 ? r106152 : r106159;
        return r106160;
}

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 z < -3.2442429541128636e-146 or 1.2816221810803726e+26 < z

    1. Initial program 6.4

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

    2. Simplified6.4

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

    4. Applied associate-*l*6.5

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

    6. Applied associate-*l*6.6

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

    if -3.2442429541128636e-146 < z < 1.2816221810803726e+26

    1. Initial program 5.2

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

    2. Simplified5.2

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

    4. Applied associate-*l*5.2

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

    5. Taylor expanded around inf 1.1

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

    6. Simplified1.1

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

  4. Final simplification4.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.24424295411286357321282707929428675159 \cdot 10^{-146} \lor \neg \left(z \le 128162218108037256959754240\right):\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(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)))