Average Error: 4.9 → 3.3
Time: 56.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.547922086558821 \cdot 10^{-88}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \le 5.279639422401091 \cdot 10^{-09}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(\left(x \cdot 18.0\right) \cdot y\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.547922086558821 \cdot 10^{-88}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\

\mathbf{elif}\;t \le 5.279639422401091 \cdot 10^{-09}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(\left(x \cdot 18.0\right) \cdot y\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\

\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 r20250063 = x;
        double r20250064 = 18.0;
        double r20250065 = r20250063 * r20250064;
        double r20250066 = y;
        double r20250067 = r20250065 * r20250066;
        double r20250068 = z;
        double r20250069 = r20250067 * r20250068;
        double r20250070 = t;
        double r20250071 = r20250069 * r20250070;
        double r20250072 = a;
        double r20250073 = 4.0;
        double r20250074 = r20250072 * r20250073;
        double r20250075 = r20250074 * r20250070;
        double r20250076 = r20250071 - r20250075;
        double r20250077 = b;
        double r20250078 = c;
        double r20250079 = r20250077 * r20250078;
        double r20250080 = r20250076 + r20250079;
        double r20250081 = r20250063 * r20250073;
        double r20250082 = i;
        double r20250083 = r20250081 * r20250082;
        double r20250084 = r20250080 - r20250083;
        double r20250085 = j;
        double r20250086 = 27.0;
        double r20250087 = r20250085 * r20250086;
        double r20250088 = k;
        double r20250089 = r20250087 * r20250088;
        double r20250090 = r20250084 - r20250089;
        return r20250090;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r20250091 = t;
        double r20250092 = -2.547922086558821e-88;
        bool r20250093 = r20250091 <= r20250092;
        double r20250094 = b;
        double r20250095 = c;
        double r20250096 = r20250094 * r20250095;
        double r20250097 = x;
        double r20250098 = 18.0;
        double r20250099 = r20250097 * r20250098;
        double r20250100 = y;
        double r20250101 = r20250099 * r20250100;
        double r20250102 = z;
        double r20250103 = r20250101 * r20250102;
        double r20250104 = r20250103 * r20250091;
        double r20250105 = a;
        double r20250106 = 4.0;
        double r20250107 = r20250105 * r20250106;
        double r20250108 = r20250107 * r20250091;
        double r20250109 = r20250104 - r20250108;
        double r20250110 = r20250096 + r20250109;
        double r20250111 = r20250106 * r20250097;
        double r20250112 = i;
        double r20250113 = r20250111 * r20250112;
        double r20250114 = r20250110 - r20250113;
        double r20250115 = 27.0;
        double r20250116 = j;
        double r20250117 = k;
        double r20250118 = r20250116 * r20250117;
        double r20250119 = r20250115 * r20250118;
        double r20250120 = r20250114 - r20250119;
        double r20250121 = 5.279639422401091e-09;
        bool r20250122 = r20250091 <= r20250121;
        double r20250123 = r20250091 * r20250102;
        double r20250124 = r20250123 * r20250101;
        double r20250125 = r20250124 - r20250108;
        double r20250126 = r20250096 + r20250125;
        double r20250127 = r20250126 - r20250113;
        double r20250128 = r20250115 * r20250117;
        double r20250129 = r20250128 * r20250116;
        double r20250130 = r20250127 - r20250129;
        double r20250131 = r20250100 * r20250102;
        double r20250132 = r20250099 * r20250131;
        double r20250133 = r20250091 * r20250132;
        double r20250134 = r20250133 - r20250108;
        double r20250135 = r20250096 + r20250134;
        double r20250136 = r20250135 - r20250113;
        double r20250137 = r20250136 - r20250129;
        double r20250138 = r20250122 ? r20250130 : r20250137;
        double r20250139 = r20250093 ? r20250120 : r20250138;
        return r20250139;
}

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 < -2.547922086558821e-88

    1. Initial program 2.6

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*2.7

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]

    4. Taylor expanded around 0 2.6

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{27.0 \cdot \left(j \cdot k\right)}\]

    if -2.547922086558821e-88 < t < 5.279639422401091e-09

    1. Initial program 7.2

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*7.2

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]
    4. Using strategy rm

    5. Applied associate-*l*4.1

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    if 5.279639422401091e-09 < t

    1. Initial program 1.7

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*1.7

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]
    4. Using strategy rm

    5. Applied associate-*l*2.3

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right)\right)} \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.547922086558821 \cdot 10^{-88}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \le 5.279639422401091 \cdot 10^{-09}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot z\right) \cdot \left(\left(x \cdot 18.0\right) \cdot y\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(\left(x \cdot 18.0\right) \cdot \left(y \cdot z\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(4.0 \cdot x\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \end{array}\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(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)))