Average Error: 5.7 → 5.5
Time: 6.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.0971657083756821 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(\sqrt[3]{j \cdot \left(27 \cdot k\right)} \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right) \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right)\right)\\ \mathbf{elif}\;t \le 3.49457155414947748 \cdot 10^{-145}:\\ \;\;\;\;0 + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]
\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 -2.0971657083756821 \cdot 10^{-234}:\\
\;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(\sqrt[3]{j \cdot \left(27 \cdot k\right)} \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right) \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right)\right)\\

\mathbf{elif}\;t \le 3.49457155414947748 \cdot 10^{-145}:\\
\;\;\;\;0 + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(j \cdot 27\right) \cdot k\right)\right)\\

\mathbf{else}:\\
\;\;\;\;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)\\

\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 r138200 = x;
        double r138201 = 18.0;
        double r138202 = r138200 * r138201;
        double r138203 = y;
        double r138204 = r138202 * r138203;
        double r138205 = z;
        double r138206 = r138204 * r138205;
        double r138207 = t;
        double r138208 = r138206 * r138207;
        double r138209 = a;
        double r138210 = 4.0;
        double r138211 = r138209 * r138210;
        double r138212 = r138211 * r138207;
        double r138213 = r138208 - r138212;
        double r138214 = b;
        double r138215 = c;
        double r138216 = r138214 * r138215;
        double r138217 = r138213 + r138216;
        double r138218 = r138200 * r138210;
        double r138219 = i;
        double r138220 = r138218 * r138219;
        double r138221 = r138217 - r138220;
        double r138222 = j;
        double r138223 = 27.0;
        double r138224 = r138222 * r138223;
        double r138225 = k;
        double r138226 = r138224 * r138225;
        double r138227 = r138221 - r138226;
        return r138227;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r138228 = t;
        double r138229 = -2.097165708375682e-234;
        bool r138230 = r138228 <= r138229;
        double r138231 = x;
        double r138232 = 18.0;
        double r138233 = y;
        double r138234 = r138232 * r138233;
        double r138235 = r138231 * r138234;
        double r138236 = z;
        double r138237 = r138235 * r138236;
        double r138238 = a;
        double r138239 = 4.0;
        double r138240 = r138238 * r138239;
        double r138241 = r138237 - r138240;
        double r138242 = r138228 * r138241;
        double r138243 = b;
        double r138244 = c;
        double r138245 = r138243 * r138244;
        double r138246 = i;
        double r138247 = r138239 * r138246;
        double r138248 = r138231 * r138247;
        double r138249 = j;
        double r138250 = 27.0;
        double r138251 = k;
        double r138252 = r138250 * r138251;
        double r138253 = r138249 * r138252;
        double r138254 = cbrt(r138253);
        double r138255 = r138254 * r138254;
        double r138256 = r138255 * r138254;
        double r138257 = r138248 + r138256;
        double r138258 = r138245 - r138257;
        double r138259 = r138242 + r138258;
        double r138260 = 3.4945715541494775e-145;
        bool r138261 = r138228 <= r138260;
        double r138262 = 0.0;
        double r138263 = r138249 * r138250;
        double r138264 = r138263 * r138251;
        double r138265 = r138248 + r138264;
        double r138266 = r138245 - r138265;
        double r138267 = r138262 + r138266;
        double r138268 = r138231 * r138232;
        double r138269 = r138268 * r138233;
        double r138270 = r138269 * r138236;
        double r138271 = r138270 - r138240;
        double r138272 = r138228 * r138271;
        double r138273 = r138231 * r138239;
        double r138274 = r138273 * r138246;
        double r138275 = r138274 + r138264;
        double r138276 = r138245 - r138275;
        double r138277 = r138272 + r138276;
        double r138278 = r138261 ? r138267 : r138277;
        double r138279 = r138230 ? r138259 : r138278;
        return r138279;
}

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 < -2.097165708375682e-234

    1. Initial program 4.6

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

    2. Simplified4.6

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

    4. Applied associate-*l*4.7

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

    6. Applied associate-*l*4.7

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

    8. Applied associate-*l*4.7

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

    10. Applied add-cube-cbrt5.0

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

    if -2.097165708375682e-234 < t < 3.4945715541494775e-145

    1. Initial program 10.3

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

    2. Simplified10.3

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

    4. Applied associate-*l*10.2

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

    6. Applied associate-*l*10.3

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

    7. Taylor expanded around 0 8.8

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

    if 3.4945715541494775e-145 < t

    1. Initial program 3.5

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

    2. Simplified3.5

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

  4. Final simplification5.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.0971657083756821 \cdot 10^{-234}:\\ \;\;\;\;t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(\sqrt[3]{j \cdot \left(27 \cdot k\right)} \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right) \cdot \sqrt[3]{j \cdot \left(27 \cdot k\right)}\right)\right)\\ \mathbf{elif}\;t \le 3.49457155414947748 \cdot 10^{-145}:\\ \;\;\;\;0 + \left(b \cdot c - \left(x \cdot \left(4 \cdot i\right) + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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)))