Average Error: 5.3 → 6.2
Time: 7.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 7.0669981561857078 \cdot 10^{-218} \lor \neg \left(k \le 4.00595738363528446 \cdot 10^{-73}\right):\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]
\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}\;k \le 7.0669981561857078 \cdot 10^{-218} \lor \neg \left(k \le 4.00595738363528446 \cdot 10^{-73}\right):\\
\;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \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 r127195 = x;
        double r127196 = 18.0;
        double r127197 = r127195 * r127196;
        double r127198 = y;
        double r127199 = r127197 * r127198;
        double r127200 = z;
        double r127201 = r127199 * r127200;
        double r127202 = t;
        double r127203 = r127201 * r127202;
        double r127204 = a;
        double r127205 = 4.0;
        double r127206 = r127204 * r127205;
        double r127207 = r127206 * r127202;
        double r127208 = r127203 - r127207;
        double r127209 = b;
        double r127210 = c;
        double r127211 = r127209 * r127210;
        double r127212 = r127208 + r127211;
        double r127213 = r127195 * r127205;
        double r127214 = i;
        double r127215 = r127213 * r127214;
        double r127216 = r127212 - r127215;
        double r127217 = j;
        double r127218 = 27.0;
        double r127219 = r127217 * r127218;
        double r127220 = k;
        double r127221 = r127219 * r127220;
        double r127222 = r127216 - r127221;
        return r127222;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r127223 = k;
        double r127224 = 7.066998156185708e-218;
        bool r127225 = r127223 <= r127224;
        double r127226 = 4.0059573836352845e-73;
        bool r127227 = r127223 <= r127226;
        double r127228 = !r127227;
        bool r127229 = r127225 || r127228;
        double r127230 = t;
        double r127231 = x;
        double r127232 = 18.0;
        double r127233 = r127231 * r127232;
        double r127234 = y;
        double r127235 = r127233 * r127234;
        double r127236 = z;
        double r127237 = r127235 * r127236;
        double r127238 = a;
        double r127239 = 4.0;
        double r127240 = r127238 * r127239;
        double r127241 = r127237 - r127240;
        double r127242 = r127230 * r127241;
        double r127243 = b;
        double r127244 = c;
        double r127245 = r127243 * r127244;
        double r127246 = r127231 * r127239;
        double r127247 = i;
        double r127248 = r127246 * r127247;
        double r127249 = j;
        double r127250 = 27.0;
        double r127251 = r127250 * r127223;
        double r127252 = r127249 * r127251;
        double r127253 = r127248 + r127252;
        double r127254 = r127245 - r127253;
        double r127255 = r127242 + r127254;
        double r127256 = 0.0;
        double r127257 = r127256 - r127240;
        double r127258 = r127230 * r127257;
        double r127259 = r127249 * r127250;
        double r127260 = r127259 * r127223;
        double r127261 = r127248 + r127260;
        double r127262 = r127245 - r127261;
        double r127263 = r127258 + r127262;
        double r127264 = r127229 ? r127255 : r127263;
        return r127264;
}

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 k < 7.066998156185708e-218 or 4.0059573836352845e-73 < k

    1. Initial program 5.4

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

    2. Simplified5.4

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

    4. Applied associate-*l*5.4

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

    if 7.066998156185708e-218 < k < 4.0059573836352845e-73

    1. Initial program 5.0

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

    2. Simplified5.0

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

    3. Taylor expanded around 0 11.1

      \[\leadsto t \cdot \left(\color{blue}{0} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 7.0669981561857078 \cdot 10^{-218} \lor \neg \left(k \le 4.00595738363528446 \cdot 10^{-73}\right):\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(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)))