Average Error: 5.6 → 4.4
Time: 16.3s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.926582951120756855854659732544200131707 \cdot 10^{-145}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{elif}\;t \le 4.57862036269468503222749585585464675082 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]
\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 -5.926582951120756855854659732544200131707 \cdot 10^{-145}:\\
\;\;\;\;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(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(27 \cdot k\right)\right)\right)\right)\\

\mathbf{elif}\;t \le 4.57862036269468503222749585585464675082 \cdot 10^{-124}:\\
\;\;\;\;t \cdot \left(0 - 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)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\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 r126520 = x;
        double r126521 = 18.0;
        double r126522 = r126520 * r126521;
        double r126523 = y;
        double r126524 = r126522 * r126523;
        double r126525 = z;
        double r126526 = r126524 * r126525;
        double r126527 = t;
        double r126528 = r126526 * r126527;
        double r126529 = a;
        double r126530 = 4.0;
        double r126531 = r126529 * r126530;
        double r126532 = r126531 * r126527;
        double r126533 = r126528 - r126532;
        double r126534 = b;
        double r126535 = c;
        double r126536 = r126534 * r126535;
        double r126537 = r126533 + r126536;
        double r126538 = r126520 * r126530;
        double r126539 = i;
        double r126540 = r126538 * r126539;
        double r126541 = r126537 - r126540;
        double r126542 = j;
        double r126543 = 27.0;
        double r126544 = r126542 * r126543;
        double r126545 = k;
        double r126546 = r126544 * r126545;
        double r126547 = r126541 - r126546;
        return r126547;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r126548 = t;
        double r126549 = -5.926582951120757e-145;
        bool r126550 = r126548 <= r126549;
        double r126551 = x;
        double r126552 = 18.0;
        double r126553 = r126551 * r126552;
        double r126554 = y;
        double r126555 = r126553 * r126554;
        double r126556 = z;
        double r126557 = r126555 * r126556;
        double r126558 = a;
        double r126559 = 4.0;
        double r126560 = r126558 * r126559;
        double r126561 = r126557 - r126560;
        double r126562 = r126548 * r126561;
        double r126563 = b;
        double r126564 = c;
        double r126565 = r126563 * r126564;
        double r126566 = r126551 * r126559;
        double r126567 = i;
        double r126568 = r126566 * r126567;
        double r126569 = j;
        double r126570 = cbrt(r126569);
        double r126571 = r126570 * r126570;
        double r126572 = 27.0;
        double r126573 = k;
        double r126574 = r126572 * r126573;
        double r126575 = r126570 * r126574;
        double r126576 = r126571 * r126575;
        double r126577 = r126568 + r126576;
        double r126578 = r126565 - r126577;
        double r126579 = r126562 + r126578;
        double r126580 = 4.578620362694685e-124;
        bool r126581 = r126548 <= r126580;
        double r126582 = 0.0;
        double r126583 = r126582 - r126560;
        double r126584 = r126548 * r126583;
        double r126585 = r126569 * r126572;
        double r126586 = r126585 * r126573;
        double r126587 = r126568 + r126586;
        double r126588 = r126565 - r126587;
        double r126589 = r126584 + r126588;
        double r126590 = cbrt(r126556);
        double r126591 = r126590 * r126590;
        double r126592 = r126555 * r126591;
        double r126593 = r126592 * r126590;
        double r126594 = r126593 - r126560;
        double r126595 = r126548 * r126594;
        double r126596 = r126569 * r126574;
        double r126597 = r126568 + r126596;
        double r126598 = r126565 - r126597;
        double r126599 = r126595 + r126598;
        double r126600 = r126581 ? r126589 : r126599;
        double r126601 = r126550 ? r126579 : r126600;
        return r126601;
}

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 < -5.926582951120757e-145

    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. Using strategy rm

    4. Applied associate-*l*3.4

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

    6. Applied add-cube-cbrt3.7

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

    7. Applied associate-*l*3.7

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

    if -5.926582951120757e-145 < t < 4.578620362694685e-124

    1. Initial program 9.4

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

    2. Simplified9.4

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

    3. Taylor expanded around 0 6.0

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

    if 4.578620362694685e-124 < t

    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

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

    4. Applied associate-*l*3.2

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

    6. Applied add-cube-cbrt3.3

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

    7. Applied associate-*r*3.3

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

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.926582951120756855854659732544200131707 \cdot 10^{-145}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \left(\sqrt[3]{j} \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{elif}\;t \le 4.57862036269468503222749585585464675082 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019318 
(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)))