Average Error: 3.8 → 0.8
Time: 19.1s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(t \cdot z\right) \cdot \left(y \cdot 9\right)\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.379137651611160183029917607616711028297 \cdot 10^{96}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\sqrt{27} \cdot b\right) \cdot a\right) \cdot \sqrt{27} - \left(t \cdot \left(z \cdot 9\right)\right) \cdot y\right) + x \cdot 2\\ \end{array}\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\
\;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(t \cdot z\right) \cdot \left(y \cdot 9\right)\right)\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.379137651611160183029917607616711028297 \cdot 10^{96}:\\
\;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(27 \cdot b\right) \cdot a\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\sqrt{27} \cdot b\right) \cdot a\right) \cdot \sqrt{27} - \left(t \cdot \left(z \cdot 9\right)\right) \cdot y\right) + x \cdot 2\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r34904443 = x;
        double r34904444 = 2.0;
        double r34904445 = r34904443 * r34904444;
        double r34904446 = y;
        double r34904447 = 9.0;
        double r34904448 = r34904446 * r34904447;
        double r34904449 = z;
        double r34904450 = r34904448 * r34904449;
        double r34904451 = t;
        double r34904452 = r34904450 * r34904451;
        double r34904453 = r34904445 - r34904452;
        double r34904454 = a;
        double r34904455 = 27.0;
        double r34904456 = r34904454 * r34904455;
        double r34904457 = b;
        double r34904458 = r34904456 * r34904457;
        double r34904459 = r34904453 + r34904458;
        return r34904459;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r34904460 = y;
        double r34904461 = 9.0;
        double r34904462 = r34904460 * r34904461;
        double r34904463 = z;
        double r34904464 = r34904462 * r34904463;
        double r34904465 = -inf.0;
        bool r34904466 = r34904464 <= r34904465;
        double r34904467 = 27.0;
        double r34904468 = a;
        double r34904469 = r34904467 * r34904468;
        double r34904470 = b;
        double r34904471 = r34904469 * r34904470;
        double r34904472 = x;
        double r34904473 = 2.0;
        double r34904474 = r34904472 * r34904473;
        double r34904475 = t;
        double r34904476 = r34904475 * r34904463;
        double r34904477 = r34904476 * r34904462;
        double r34904478 = r34904474 - r34904477;
        double r34904479 = r34904471 + r34904478;
        double r34904480 = 2.37913765161116e+96;
        bool r34904481 = r34904464 <= r34904480;
        double r34904482 = r34904464 * r34904475;
        double r34904483 = r34904474 - r34904482;
        double r34904484 = r34904467 * r34904470;
        double r34904485 = r34904484 * r34904468;
        double r34904486 = r34904483 + r34904485;
        double r34904487 = sqrt(r34904467);
        double r34904488 = r34904487 * r34904470;
        double r34904489 = r34904488 * r34904468;
        double r34904490 = r34904489 * r34904487;
        double r34904491 = r34904463 * r34904461;
        double r34904492 = r34904475 * r34904491;
        double r34904493 = r34904492 * r34904460;
        double r34904494 = r34904490 - r34904493;
        double r34904495 = r34904494 + r34904474;
        double r34904496 = r34904481 ? r34904486 : r34904495;
        double r34904497 = r34904466 ? r34904479 : r34904496;
        return r34904497;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.8
Target2.8
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -inf.0

    1. Initial program 64.0

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*1.4

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    if -inf.0 < (* (* y 9.0) z) < 2.37913765161116e+96

    1. Initial program 0.4

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*0.4

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)}\]

    if 2.37913765161116e+96 < (* (* y 9.0) z)

    1. Initial program 14.5

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied sub-neg14.5

      \[\leadsto \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b\]

    4. Applied associate-+l+14.5

      \[\leadsto \color{blue}{x \cdot 2 + \left(\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\right)}\]

    5. Simplified3.5

      \[\leadsto x \cdot 2 + \color{blue}{\left(\left(a \cdot b\right) \cdot 27 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)}\]
    6. Using strategy rm

    7. Applied add-sqr-sqrt3.5

      \[\leadsto x \cdot 2 + \left(\left(a \cdot b\right) \cdot \color{blue}{\left(\sqrt{27} \cdot \sqrt{27}\right)} - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\]

    8. Applied associate-*r*3.5

      \[\leadsto x \cdot 2 + \left(\color{blue}{\left(\left(a \cdot b\right) \cdot \sqrt{27}\right) \cdot \sqrt{27}} - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\]
    9. Using strategy rm

    10. Applied *-un-lft-identity3.5

      \[\leadsto x \cdot 2 + \left(\left(\left(a \cdot b\right) \cdot \sqrt{27}\right) \cdot \sqrt{\color{blue}{1 \cdot 27}} - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\]

    11. Applied sqrt-prod3.5

      \[\leadsto x \cdot 2 + \left(\left(\left(a \cdot b\right) \cdot \sqrt{27}\right) \cdot \color{blue}{\left(\sqrt{1} \cdot \sqrt{27}\right)} - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\]

    12. Applied associate-*r*3.5

      \[\leadsto x \cdot 2 + \left(\color{blue}{\left(\left(\left(a \cdot b\right) \cdot \sqrt{27}\right) \cdot \sqrt{1}\right) \cdot \sqrt{27}} - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\]

    13. Simplified3.5

      \[\leadsto x \cdot 2 + \left(\color{blue}{\left(\left(b \cdot \sqrt{27}\right) \cdot a\right)} \cdot \sqrt{27} - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(t \cdot z\right) \cdot \left(y \cdot 9\right)\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.379137651611160183029917607616711028297 \cdot 10^{96}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\sqrt{27} \cdot b\right) \cdot a\right) \cdot \sqrt{27} - \left(t \cdot \left(z \cdot 9\right)\right) \cdot y\right) + x \cdot 2\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))