Average Error: 5.6 → 6.7
Time: 25.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \le -2.954442886009252531198288738982951568249 \cdot 10^{-102}:\\ \;\;\;\;\left(\left(-a \cdot 4\right) \cdot t + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \end{array}\]
\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}\;\left(j \cdot 27\right) \cdot k \le -2.954442886009252531198288738982951568249 \cdot 10^{-102}:\\
\;\;\;\;\left(\left(-a \cdot 4\right) \cdot t + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(k \cdot j\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\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 + j \cdot \left(27 \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 r26395 = x;
        double r26396 = 18.0;
        double r26397 = r26395 * r26396;
        double r26398 = y;
        double r26399 = r26397 * r26398;
        double r26400 = z;
        double r26401 = r26399 * r26400;
        double r26402 = t;
        double r26403 = r26401 * r26402;
        double r26404 = a;
        double r26405 = 4.0;
        double r26406 = r26404 * r26405;
        double r26407 = r26406 * r26402;
        double r26408 = r26403 - r26407;
        double r26409 = b;
        double r26410 = c;
        double r26411 = r26409 * r26410;
        double r26412 = r26408 + r26411;
        double r26413 = r26395 * r26405;
        double r26414 = i;
        double r26415 = r26413 * r26414;
        double r26416 = r26412 - r26415;
        double r26417 = j;
        double r26418 = 27.0;
        double r26419 = r26417 * r26418;
        double r26420 = k;
        double r26421 = r26419 * r26420;
        double r26422 = r26416 - r26421;
        return r26422;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r26423 = j;
        double r26424 = 27.0;
        double r26425 = r26423 * r26424;
        double r26426 = k;
        double r26427 = r26425 * r26426;
        double r26428 = -2.9544428860092525e-102;
        bool r26429 = r26427 <= r26428;
        double r26430 = a;
        double r26431 = 4.0;
        double r26432 = r26430 * r26431;
        double r26433 = -r26432;
        double r26434 = t;
        double r26435 = r26433 * r26434;
        double r26436 = b;
        double r26437 = c;
        double r26438 = r26436 * r26437;
        double r26439 = r26435 + r26438;
        double r26440 = x;
        double r26441 = r26440 * r26431;
        double r26442 = i;
        double r26443 = r26441 * r26442;
        double r26444 = sqrt(r26424);
        double r26445 = r26426 * r26423;
        double r26446 = r26444 * r26445;
        double r26447 = r26444 * r26446;
        double r26448 = r26443 + r26447;
        double r26449 = r26439 - r26448;
        double r26450 = 18.0;
        double r26451 = r26440 * r26450;
        double r26452 = y;
        double r26453 = r26451 * r26452;
        double r26454 = z;
        double r26455 = r26453 * r26454;
        double r26456 = r26455 - r26432;
        double r26457 = r26434 * r26456;
        double r26458 = r26457 + r26438;
        double r26459 = r26424 * r26426;
        double r26460 = r26423 * r26459;
        double r26461 = r26443 + r26460;
        double r26462 = r26458 - r26461;
        double r26463 = r26429 ? r26449 : r26462;
        return r26463;
}

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 (* (* j 27.0) k) < -2.9544428860092525e-102

    1. Initial program 5.1

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

    2. Simplified5.1

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

    4. Applied associate-*l*5.1

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

    5. Taylor expanded around 0 5.0

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

    7. Applied add-sqr-sqrt5.0

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

    8. Applied associate-*l*5.1

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

    9. Taylor expanded around 0 8.7

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

    if -2.9544428860092525e-102 < (* (* j 27.0) k)

    1. Initial program 5.8

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

    2. Simplified5.8

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

    4. Applied associate-*l*5.8

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

  4. Final simplification6.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \le -2.954442886009252531198288738982951568249 \cdot 10^{-102}:\\ \;\;\;\;\left(\left(-a \cdot 4\right) \cdot t + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(k \cdot j\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019315 
(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)))