Average Error: 5.6 → 5.7
Time: 31.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;i \le -3.670913261354025603289537322978303432162 \cdot 10^{86}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array}\]
\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}\;i \le -3.670913261354025603289537322978303432162 \cdot 10^{86}:\\
\;\;\;\;\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)\\

\mathbf{else}:\\
\;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + 27 \cdot \left(k \cdot j\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 r106312 = x;
        double r106313 = 18.0;
        double r106314 = r106312 * r106313;
        double r106315 = y;
        double r106316 = r106314 * r106315;
        double r106317 = z;
        double r106318 = r106316 * r106317;
        double r106319 = t;
        double r106320 = r106318 * r106319;
        double r106321 = a;
        double r106322 = 4.0;
        double r106323 = r106321 * r106322;
        double r106324 = r106323 * r106319;
        double r106325 = r106320 - r106324;
        double r106326 = b;
        double r106327 = c;
        double r106328 = r106326 * r106327;
        double r106329 = r106325 + r106328;
        double r106330 = r106312 * r106322;
        double r106331 = i;
        double r106332 = r106330 * r106331;
        double r106333 = r106329 - r106332;
        double r106334 = j;
        double r106335 = 27.0;
        double r106336 = r106334 * r106335;
        double r106337 = k;
        double r106338 = r106336 * r106337;
        double r106339 = r106333 - r106338;
        return r106339;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r106340 = i;
        double r106341 = -3.6709132613540256e+86;
        bool r106342 = r106340 <= r106341;
        double r106343 = t;
        double r106344 = x;
        double r106345 = y;
        double r106346 = 18.0;
        double r106347 = r106345 * r106346;
        double r106348 = r106344 * r106347;
        double r106349 = z;
        double r106350 = r106348 * r106349;
        double r106351 = a;
        double r106352 = 4.0;
        double r106353 = r106351 * r106352;
        double r106354 = r106350 - r106353;
        double r106355 = r106343 * r106354;
        double r106356 = b;
        double r106357 = c;
        double r106358 = r106356 * r106357;
        double r106359 = r106355 + r106358;
        double r106360 = r106344 * r106352;
        double r106361 = r106360 * r106340;
        double r106362 = j;
        double r106363 = 27.0;
        double r106364 = k;
        double r106365 = r106363 * r106364;
        double r106366 = r106362 * r106365;
        double r106367 = r106361 + r106366;
        double r106368 = r106359 - r106367;
        double r106369 = r106344 * r106346;
        double r106370 = r106349 * r106345;
        double r106371 = r106369 * r106370;
        double r106372 = r106371 - r106353;
        double r106373 = r106343 * r106372;
        double r106374 = r106373 + r106358;
        double r106375 = r106364 * r106362;
        double r106376 = r106363 * r106375;
        double r106377 = r106361 + r106376;
        double r106378 = r106374 - r106377;
        double r106379 = r106342 ? r106368 : r106378;
        return r106379;
}

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 i < -3.6709132613540256e+86

    1. Initial program 3.1

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

    2. Simplified3.1

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

    4. Applied associate-*l*3.3

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

    6. Applied associate-*l*3.3

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

    7. Simplified3.3

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

    if -3.6709132613540256e+86 < i

    1. Initial program 6.1

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

    2. Simplified6.1

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

    4. Applied associate-*l*6.1

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

    6. Applied associate-*l*6.3

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

    7. Simplified6.3

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

    9. Applied pow16.3

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

    10. Applied pow16.3

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

    11. Applied pow-prod-down6.3

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

    12. Applied pow16.3

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

    13. Applied pow-prod-down6.3

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

    14. Simplified6.2

      \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + {\color{blue}{\left(27 \cdot \left(k \cdot j\right)\right)}}^{1}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;i \le -3.670913261354025603289537322978303432162 \cdot 10^{86}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot \left(y \cdot 18\right)\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot y\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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)))