Average Error: 5.6 → 4.8
Time: 24.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.556070220324067637922052949506160381905 \cdot 10^{-307}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \mathbf{elif}\;t \le 4.461860870917308238894980463712832079364 \cdot 10^{-94}:\\ \;\;\;\;\left(\left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \end{array}\]
\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 -2.556070220324067637922052949506160381905 \cdot 10^{-307}:\\
\;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\

\mathbf{elif}\;t \le 4.461860870917308238894980463712832079364 \cdot 10^{-94}:\\
\;\;\;\;\left(\left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\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 r40228518 = x;
        double r40228519 = 18.0;
        double r40228520 = r40228518 * r40228519;
        double r40228521 = y;
        double r40228522 = r40228520 * r40228521;
        double r40228523 = z;
        double r40228524 = r40228522 * r40228523;
        double r40228525 = t;
        double r40228526 = r40228524 * r40228525;
        double r40228527 = a;
        double r40228528 = 4.0;
        double r40228529 = r40228527 * r40228528;
        double r40228530 = r40228529 * r40228525;
        double r40228531 = r40228526 - r40228530;
        double r40228532 = b;
        double r40228533 = c;
        double r40228534 = r40228532 * r40228533;
        double r40228535 = r40228531 + r40228534;
        double r40228536 = r40228518 * r40228528;
        double r40228537 = i;
        double r40228538 = r40228536 * r40228537;
        double r40228539 = r40228535 - r40228538;
        double r40228540 = j;
        double r40228541 = 27.0;
        double r40228542 = r40228540 * r40228541;
        double r40228543 = k;
        double r40228544 = r40228542 * r40228543;
        double r40228545 = r40228539 - r40228544;
        return r40228545;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r40228546 = t;
        double r40228547 = -2.5560702203240676e-307;
        bool r40228548 = r40228546 <= r40228547;
        double r40228549 = b;
        double r40228550 = c;
        double r40228551 = r40228549 * r40228550;
        double r40228552 = 4.0;
        double r40228553 = i;
        double r40228554 = x;
        double r40228555 = r40228553 * r40228554;
        double r40228556 = r40228552 * r40228555;
        double r40228557 = j;
        double r40228558 = 27.0;
        double r40228559 = r40228557 * r40228558;
        double r40228560 = k;
        double r40228561 = r40228559 * r40228560;
        double r40228562 = r40228556 + r40228561;
        double r40228563 = r40228551 - r40228562;
        double r40228564 = z;
        double r40228565 = 18.0;
        double r40228566 = r40228564 * r40228565;
        double r40228567 = r40228554 * r40228566;
        double r40228568 = y;
        double r40228569 = r40228567 * r40228568;
        double r40228570 = a;
        double r40228571 = r40228570 * r40228552;
        double r40228572 = r40228569 - r40228571;
        double r40228573 = r40228546 * r40228572;
        double r40228574 = r40228563 + r40228573;
        double r40228575 = 4.461860870917308e-94;
        bool r40228576 = r40228546 <= r40228575;
        double r40228577 = r40228565 * r40228554;
        double r40228578 = r40228577 * r40228568;
        double r40228579 = r40228546 * r40228564;
        double r40228580 = r40228578 * r40228579;
        double r40228581 = r40228546 * r40228571;
        double r40228582 = r40228580 - r40228581;
        double r40228583 = r40228582 + r40228551;
        double r40228584 = r40228554 * r40228552;
        double r40228585 = r40228584 * r40228553;
        double r40228586 = r40228583 - r40228585;
        double r40228587 = r40228560 * r40228558;
        double r40228588 = r40228587 * r40228557;
        double r40228589 = r40228586 - r40228588;
        double r40228590 = r40228576 ? r40228589 : r40228574;
        double r40228591 = r40228548 ? r40228574 : r40228590;
        return r40228591;
}

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

Target

Original5.6
Target1.5
Herbie4.8
\[\begin{array}{l} \mathbf{if}\;t \lt -1.62108153975413982700795070153457058168 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.6802794380522243500308832153677940369:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.5560702203240676e-307 or 4.461860870917308e-94 < t

    1. Initial program 4.7

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

    2. Simplified4.7

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

    4. Applied associate-*l*5.0

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

    if -2.5560702203240676e-307 < t < 4.461860870917308e-94

    1. Initial program 8.4

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

    3. Applied associate-*l*8.4

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

    5. Applied associate-*l*4.0

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

  4. Final simplification4.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.556070220324067637922052949506160381905 \cdot 10^{-307}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \mathbf{elif}\;t \le 4.461860870917308238894980463712832079364 \cdot 10^{-94}:\\ \;\;\;\;\left(\left(\left(\left(\left(18 \cdot x\right) \cdot y\right) \cdot \left(t \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot 27\right) \cdot k\right)\right) + t \cdot \left(\left(x \cdot \left(z \cdot 18\right)\right) \cdot y - a \cdot 4\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))