Average Error: 5.7 → 1.6
Time: 25.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\left(t \cdot y\right) \cdot z\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x}, 18, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(4, \mathsf{fma}\left(t, a, x \cdot i\right), j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 1.583419617970655285712273062224011067798 \cdot 10^{284}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot \left(z \cdot y\right)\right) \cdot x, 18, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(4, \mathsf{fma}\left(t, a, x \cdot i\right), j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \end{array}\]
\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}\;\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 = -\infty:\\
\;\;\;\;\mathsf{fma}\left(\left(\left(\left(t \cdot y\right) \cdot z\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x}, 18, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(4, \mathsf{fma}\left(t, a, x \cdot i\right), j \cdot \left(27 \cdot k\right)\right)\right)\right)\\

\mathbf{elif}\;\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 \le 1.583419617970655285712273062224011067798 \cdot 10^{284}:\\
\;\;\;\;\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\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\left(t \cdot \left(z \cdot y\right)\right) \cdot x, 18, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(4, \mathsf{fma}\left(t, a, x \cdot i\right), j \cdot \left(27 \cdot k\right)\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 r130548 = x;
        double r130549 = 18.0;
        double r130550 = r130548 * r130549;
        double r130551 = y;
        double r130552 = r130550 * r130551;
        double r130553 = z;
        double r130554 = r130552 * r130553;
        double r130555 = t;
        double r130556 = r130554 * r130555;
        double r130557 = a;
        double r130558 = 4.0;
        double r130559 = r130557 * r130558;
        double r130560 = r130559 * r130555;
        double r130561 = r130556 - r130560;
        double r130562 = b;
        double r130563 = c;
        double r130564 = r130562 * r130563;
        double r130565 = r130561 + r130564;
        double r130566 = r130548 * r130558;
        double r130567 = i;
        double r130568 = r130566 * r130567;
        double r130569 = r130565 - r130568;
        double r130570 = j;
        double r130571 = 27.0;
        double r130572 = r130570 * r130571;
        double r130573 = k;
        double r130574 = r130572 * r130573;
        double r130575 = r130569 - r130574;
        return r130575;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r130576 = x;
        double r130577 = 18.0;
        double r130578 = r130576 * r130577;
        double r130579 = y;
        double r130580 = r130578 * r130579;
        double r130581 = z;
        double r130582 = r130580 * r130581;
        double r130583 = t;
        double r130584 = r130582 * r130583;
        double r130585 = a;
        double r130586 = 4.0;
        double r130587 = r130585 * r130586;
        double r130588 = r130587 * r130583;
        double r130589 = r130584 - r130588;
        double r130590 = b;
        double r130591 = c;
        double r130592 = r130590 * r130591;
        double r130593 = r130589 + r130592;
        double r130594 = r130576 * r130586;
        double r130595 = i;
        double r130596 = r130594 * r130595;
        double r130597 = r130593 - r130596;
        double r130598 = -inf.0;
        bool r130599 = r130597 <= r130598;
        double r130600 = r130583 * r130579;
        double r130601 = r130600 * r130581;
        double r130602 = cbrt(r130576);
        double r130603 = r130602 * r130602;
        double r130604 = r130601 * r130603;
        double r130605 = r130604 * r130602;
        double r130606 = r130576 * r130595;
        double r130607 = fma(r130583, r130585, r130606);
        double r130608 = j;
        double r130609 = 27.0;
        double r130610 = k;
        double r130611 = r130609 * r130610;
        double r130612 = r130608 * r130611;
        double r130613 = fma(r130586, r130607, r130612);
        double r130614 = -r130613;
        double r130615 = fma(r130591, r130590, r130614);
        double r130616 = fma(r130605, r130577, r130615);
        double r130617 = 1.5834196179706553e+284;
        bool r130618 = r130597 <= r130617;
        double r130619 = r130608 * r130609;
        double r130620 = r130619 * r130610;
        double r130621 = r130597 - r130620;
        double r130622 = r130581 * r130579;
        double r130623 = r130583 * r130622;
        double r130624 = r130623 * r130576;
        double r130625 = fma(r130624, r130577, r130615);
        double r130626 = r130618 ? r130621 : r130625;
        double r130627 = r130599 ? r130616 : r130626;
        return r130627;
}

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

Derivation

  1. Split input into 3 regimes

  2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0

    1. Initial program 64.0

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

    2. Simplified14.4

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

    4. Applied associate-*r*5.3

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

    6. Applied associate-*l*5.5

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

    8. Applied add-cube-cbrt5.9

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

    9. Applied associate-*r*5.9

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

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 1.5834196179706553e+284

    1. Initial program 0.4

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

    if 1.5834196179706553e+284 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 37.4

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

    2. Simplified12.5

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

    4. Applied associate-*r*7.6

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

    6. Applied associate-*l*7.6

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

    8. Applied *-un-lft-identity7.6

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

    9. Applied associate-*r*7.6

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

    10. Simplified13.6

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\left(t \cdot y\right) \cdot z\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x}, 18, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(4, \mathsf{fma}\left(t, a, x \cdot i\right), j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \le 1.583419617970655285712273062224011067798 \cdot 10^{284}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot \left(z \cdot y\right)\right) \cdot x, 18, \mathsf{fma}\left(c, b, -\mathsf{fma}\left(4, \mathsf{fma}\left(t, a, x \cdot i\right), j \cdot \left(27 \cdot k\right)\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(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)))