Average Error: 5.8 → 6.3
Time: 33.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \le -4.540980572012251526114420073985087439812 \cdot 10^{-316} \lor \neg \left(\left(j \cdot 27\right) \cdot k \le 2161642607386816256\right) \land \left(j \cdot 27\right) \cdot k \le 1.732330144710722980399686902944367574721 \cdot 10^{167}:\\ \;\;\;\;\left(\left(\left(18 \cdot \left(\left(t \cdot x\right) \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \sqrt{\left(j \cdot 27\right) \cdot k} \cdot \sqrt{\left(j \cdot 27\right) \cdot k}\\ \end{array}\]
\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 -4.540980572012251526114420073985087439812 \cdot 10^{-316} \lor \neg \left(\left(j \cdot 27\right) \cdot k \le 2161642607386816256\right) \land \left(j \cdot 27\right) \cdot k \le 1.732330144710722980399686902944367574721 \cdot 10^{167}:\\
\;\;\;\;\left(\left(\left(18 \cdot \left(\left(t \cdot x\right) \cdot \left(z \cdot y\right)\right) - \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\\

\mathbf{else}:\\
\;\;\;\;\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) - \sqrt{\left(j \cdot 27\right) \cdot k} \cdot \sqrt{\left(j \cdot 27\right) \cdot k}\\

\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 r82326 = x;
        double r82327 = 18.0;
        double r82328 = r82326 * r82327;
        double r82329 = y;
        double r82330 = r82328 * r82329;
        double r82331 = z;
        double r82332 = r82330 * r82331;
        double r82333 = t;
        double r82334 = r82332 * r82333;
        double r82335 = a;
        double r82336 = 4.0;
        double r82337 = r82335 * r82336;
        double r82338 = r82337 * r82333;
        double r82339 = r82334 - r82338;
        double r82340 = b;
        double r82341 = c;
        double r82342 = r82340 * r82341;
        double r82343 = r82339 + r82342;
        double r82344 = r82326 * r82336;
        double r82345 = i;
        double r82346 = r82344 * r82345;
        double r82347 = r82343 - r82346;
        double r82348 = j;
        double r82349 = 27.0;
        double r82350 = r82348 * r82349;
        double r82351 = k;
        double r82352 = r82350 * r82351;
        double r82353 = r82347 - r82352;
        return r82353;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r82354 = j;
        double r82355 = 27.0;
        double r82356 = r82354 * r82355;
        double r82357 = k;
        double r82358 = r82356 * r82357;
        double r82359 = -4.5409805720123e-316;
        bool r82360 = r82358 <= r82359;
        double r82361 = 2.1616426073868163e+18;
        bool r82362 = r82358 <= r82361;
        double r82363 = !r82362;
        double r82364 = 1.732330144710723e+167;
        bool r82365 = r82358 <= r82364;
        bool r82366 = r82363 && r82365;
        bool r82367 = r82360 || r82366;
        double r82368 = 18.0;
        double r82369 = t;
        double r82370 = x;
        double r82371 = r82369 * r82370;
        double r82372 = z;
        double r82373 = y;
        double r82374 = r82372 * r82373;
        double r82375 = r82371 * r82374;
        double r82376 = r82368 * r82375;
        double r82377 = a;
        double r82378 = 4.0;
        double r82379 = r82377 * r82378;
        double r82380 = r82379 * r82369;
        double r82381 = r82376 - r82380;
        double r82382 = b;
        double r82383 = c;
        double r82384 = r82382 * r82383;
        double r82385 = r82381 + r82384;
        double r82386 = r82370 * r82378;
        double r82387 = i;
        double r82388 = r82386 * r82387;
        double r82389 = r82385 - r82388;
        double r82390 = r82389 - r82358;
        double r82391 = r82370 * r82368;
        double r82392 = r82391 * r82373;
        double r82393 = r82392 * r82372;
        double r82394 = r82393 * r82369;
        double r82395 = r82394 - r82380;
        double r82396 = r82395 + r82384;
        double r82397 = r82396 - r82388;
        double r82398 = sqrt(r82358);
        double r82399 = r82398 * r82398;
        double r82400 = r82397 - r82399;
        double r82401 = r82367 ? r82390 : r82400;
        return r82401;
}

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) < -4.5409805720123e-316 or 2.1616426073868163e+18 < (* (* j 27.0) k) < 1.732330144710723e+167

    1. Initial program 5.9

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

    3. Applied pow15.9

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

    4. Applied pow15.9

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

    5. Applied pow15.9

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

    6. Applied pow15.9

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

    7. Applied pow15.9

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

    8. Applied pow-prod-down5.9

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

    9. Applied pow-prod-down5.9

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

    10. Applied pow-prod-down5.9

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

    11. Applied pow-prod-down5.9

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

    12. Simplified6.1

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

    14. Applied associate-*r*6.3

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

    if -4.5409805720123e-316 < (* (* j 27.0) k) < 2.1616426073868163e+18 or 1.732330144710723e+167 < (* (* j 27.0) k)

    1. Initial program 5.6

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

    3. Applied add-sqr-sqrt6.2

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

  4. Final simplification6.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \le -4.540980572012251526114420073985087439812 \cdot 10^{-316} \lor \neg \left(\left(j \cdot 27\right) \cdot k \le 2161642607386816256\right) \land \left(j \cdot 27\right) \cdot k \le 1.732330144710722980399686902944367574721 \cdot 10^{167}:\\ \;\;\;\;\left(\left(\left(18 \cdot \left(\left(t \cdot x\right) \cdot \left(z \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \sqrt{\left(j \cdot 27\right) \cdot k} \cdot \sqrt{\left(j \cdot 27\right) \cdot k}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))