Average Error: 5.6 → 4.3
Time: 24.3s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.2028576290406759 \cdot 10^{164} \lor \neg \left(t \le 3.8698264799029388 \cdot 10^{-82}\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(x \cdot \left(z \cdot y\right)\right) \cdot 18\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]
\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 -1.2028576290406759 \cdot 10^{164} \lor \neg \left(t \le 3.8698264799029388 \cdot 10^{-82}\right):\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(x \cdot \left(z \cdot y\right)\right) \cdot 18\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\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) - j \cdot \left(27 \cdot k\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 r100179 = x;
        double r100180 = 18.0;
        double r100181 = r100179 * r100180;
        double r100182 = y;
        double r100183 = r100181 * r100182;
        double r100184 = z;
        double r100185 = r100183 * r100184;
        double r100186 = t;
        double r100187 = r100185 * r100186;
        double r100188 = a;
        double r100189 = 4.0;
        double r100190 = r100188 * r100189;
        double r100191 = r100190 * r100186;
        double r100192 = r100187 - r100191;
        double r100193 = b;
        double r100194 = c;
        double r100195 = r100193 * r100194;
        double r100196 = r100192 + r100195;
        double r100197 = r100179 * r100189;
        double r100198 = i;
        double r100199 = r100197 * r100198;
        double r100200 = r100196 - r100199;
        double r100201 = j;
        double r100202 = 27.0;
        double r100203 = r100201 * r100202;
        double r100204 = k;
        double r100205 = r100203 * r100204;
        double r100206 = r100200 - r100205;
        return r100206;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r100207 = t;
        double r100208 = -1.202857629040676e+164;
        bool r100209 = r100207 <= r100208;
        double r100210 = 3.869826479902939e-82;
        bool r100211 = r100207 <= r100210;
        double r100212 = !r100211;
        bool r100213 = r100209 || r100212;
        double r100214 = b;
        double r100215 = c;
        double r100216 = r100214 * r100215;
        double r100217 = x;
        double r100218 = z;
        double r100219 = y;
        double r100220 = r100218 * r100219;
        double r100221 = r100217 * r100220;
        double r100222 = 18.0;
        double r100223 = r100221 * r100222;
        double r100224 = r100223 * r100207;
        double r100225 = a;
        double r100226 = 4.0;
        double r100227 = r100225 * r100226;
        double r100228 = r100227 * r100207;
        double r100229 = r100224 - r100228;
        double r100230 = r100216 + r100229;
        double r100231 = r100217 * r100226;
        double r100232 = i;
        double r100233 = r100231 * r100232;
        double r100234 = r100230 - r100233;
        double r100235 = j;
        double r100236 = 27.0;
        double r100237 = k;
        double r100238 = r100236 * r100237;
        double r100239 = r100235 * r100238;
        double r100240 = r100234 - r100239;
        double r100241 = r100222 * r100219;
        double r100242 = r100217 * r100241;
        double r100243 = r100218 * r100207;
        double r100244 = r100242 * r100243;
        double r100245 = r100244 - r100228;
        double r100246 = r100245 + r100216;
        double r100247 = r100246 - r100233;
        double r100248 = r100247 - r100239;
        double r100249 = r100213 ? r100240 : r100248;
        return r100249;
}

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 < -1.202857629040676e+164 or 3.869826479902939e-82 < t

    1. Initial program 2.3

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

    3. Applied associate-*l*2.4

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

    5. Applied associate-*l*2.4

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

    7. Applied pow12.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \color{blue}{{z}^{1}}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    8. Applied pow12.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(18 \cdot \color{blue}{{y}^{1}}\right)\right) \cdot {z}^{1}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    9. Applied pow12.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(\color{blue}{{18}^{1}} \cdot {y}^{1}\right)\right) \cdot {z}^{1}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    10. Applied pow-prod-down2.4

      \[\leadsto \left(\left(\left(\left(\left(x \cdot \color{blue}{{\left(18 \cdot y\right)}^{1}}\right) \cdot {z}^{1}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    11. Applied pow12.4

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{{x}^{1}} \cdot {\left(18 \cdot y\right)}^{1}\right) \cdot {z}^{1}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    12. Applied pow-prod-down2.4

      \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(x \cdot \left(18 \cdot y\right)\right)}^{1}} \cdot {z}^{1}\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    13. Applied pow-prod-down2.4

      \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z\right)}^{1}} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    14. Simplified2.9

      \[\leadsto \left(\left(\left({\color{blue}{\left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)}}^{1} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\]

    if -1.202857629040676e+164 < t < 3.869826479902939e-82

    1. Initial program 7.1

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

    3. Applied associate-*l*7.2

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

    5. Applied associate-*l*7.2

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

    7. Applied associate-*l*4.9

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

  4. Final simplification4.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.2028576290406759 \cdot 10^{164} \lor \neg \left(t \le 3.8698264799029388 \cdot 10^{-82}\right):\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(x \cdot \left(z \cdot y\right)\right) \cdot 18\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(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)))