Average Error: 5.6 → 4.7
Time: 27.2s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.1141079314986784 \cdot 10^{-44}:\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right)\\ \mathbf{elif}\;t \le 1.1312232233938015 \cdot 10^{-68}:\\ \;\;\;\;\left(t \cdot \left(-a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \end{array}\]
\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 -3.1141079314986784 \cdot 10^{-44}:\\
\;\;\;\;\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(\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}\right)\\

\mathbf{elif}\;t \le 1.1312232233938015 \cdot 10^{-68}:\\
\;\;\;\;\left(t \cdot \left(-a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(t \cdot \left(\left(x \cdot \left(y \cdot 18\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)\\

\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 r131071 = x;
        double r131072 = 18.0;
        double r131073 = r131071 * r131072;
        double r131074 = y;
        double r131075 = r131073 * r131074;
        double r131076 = z;
        double r131077 = r131075 * r131076;
        double r131078 = t;
        double r131079 = r131077 * r131078;
        double r131080 = a;
        double r131081 = 4.0;
        double r131082 = r131080 * r131081;
        double r131083 = r131082 * r131078;
        double r131084 = r131079 - r131083;
        double r131085 = b;
        double r131086 = c;
        double r131087 = r131085 * r131086;
        double r131088 = r131084 + r131087;
        double r131089 = r131071 * r131081;
        double r131090 = i;
        double r131091 = r131089 * r131090;
        double r131092 = r131088 - r131091;
        double r131093 = j;
        double r131094 = 27.0;
        double r131095 = r131093 * r131094;
        double r131096 = k;
        double r131097 = r131095 * r131096;
        double r131098 = r131092 - r131097;
        return r131098;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r131099 = t;
        double r131100 = -3.1141079314986784e-44;
        bool r131101 = r131099 <= r131100;
        double r131102 = x;
        double r131103 = 18.0;
        double r131104 = r131102 * r131103;
        double r131105 = y;
        double r131106 = r131104 * r131105;
        double r131107 = z;
        double r131108 = r131106 * r131107;
        double r131109 = a;
        double r131110 = 4.0;
        double r131111 = r131109 * r131110;
        double r131112 = r131108 - r131111;
        double r131113 = r131099 * r131112;
        double r131114 = b;
        double r131115 = c;
        double r131116 = r131114 * r131115;
        double r131117 = r131113 + r131116;
        double r131118 = r131102 * r131110;
        double r131119 = i;
        double r131120 = r131118 * r131119;
        double r131121 = j;
        double r131122 = 27.0;
        double r131123 = r131121 * r131122;
        double r131124 = k;
        double r131125 = r131123 * r131124;
        double r131126 = cbrt(r131125);
        double r131127 = r131126 * r131126;
        double r131128 = r131127 * r131126;
        double r131129 = r131120 + r131128;
        double r131130 = r131117 - r131129;
        double r131131 = 1.1312232233938015e-68;
        bool r131132 = r131099 <= r131131;
        double r131133 = -r131111;
        double r131134 = r131099 * r131133;
        double r131135 = r131134 + r131116;
        double r131136 = r131120 + r131125;
        double r131137 = r131135 - r131136;
        double r131138 = r131105 * r131103;
        double r131139 = r131102 * r131138;
        double r131140 = r131139 * r131107;
        double r131141 = r131140 - r131111;
        double r131142 = r131099 * r131141;
        double r131143 = r131142 + r131116;
        double r131144 = r131122 * r131124;
        double r131145 = r131121 * r131144;
        double r131146 = r131120 + r131145;
        double r131147 = r131143 - r131146;
        double r131148 = r131132 ? r131137 : r131147;
        double r131149 = r131101 ? r131130 : r131148;
        return r131149;
}

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 3 regimes

  2. if t < -3.1141079314986784e-44

    1. Initial program 2.0

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

    2. Simplified2.0

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

    4. Applied add-cube-cbrt2.2

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

    if -3.1141079314986784e-44 < t < 1.1312232233938015e-68

    1. Initial program 8.7

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

    2. Simplified8.7

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

    3. Taylor expanded around 0 6.8

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

    if 1.1312232233938015e-68 < t

    1. Initial program 2.4

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

    2. Simplified2.4

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

    4. Applied associate-*l*2.4

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

    6. Applied associate-*l*2.4

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

    7. Simplified2.4

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

  4. Final simplification4.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.1141079314986784 \cdot 10^{-44}:\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{\left(j \cdot 27\right) \cdot k} \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right) \cdot \sqrt[3]{\left(j \cdot 27\right) \cdot k}\right)\\ \mathbf{elif}\;t \le 1.1312232233938015 \cdot 10^{-68}:\\ \;\;\;\;\left(t \cdot \left(-a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)))