Average Error: 3.6 → 0.7
Time: 18.3s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le -4.868254455495116538116089271342050718719 \cdot 10^{284} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le 8.519303710692691346111528747466709815103 \cdot 10^{306}\right):\\ \;\;\;\;\left(2 \cdot x - \left(z \cdot t\right) \cdot \left(y \cdot 9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + \left(27 \cdot \left(b \cdot a\right) + 9 \cdot \left(\left(-z \cdot y\right) \cdot t\right)\right)\\ \end{array}\]
\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(\left(y \cdot 9\right) \cdot z\right) \cdot t \le -4.868254455495116538116089271342050718719 \cdot 10^{284} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le 8.519303710692691346111528747466709815103 \cdot 10^{306}\right):\\
\;\;\;\;\left(2 \cdot x - \left(z \cdot t\right) \cdot \left(y \cdot 9\right)\right) + a \cdot \left(27 \cdot b\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r603434 = x;
        double r603435 = 2.0;
        double r603436 = r603434 * r603435;
        double r603437 = y;
        double r603438 = 9.0;
        double r603439 = r603437 * r603438;
        double r603440 = z;
        double r603441 = r603439 * r603440;
        double r603442 = t;
        double r603443 = r603441 * r603442;
        double r603444 = r603436 - r603443;
        double r603445 = a;
        double r603446 = 27.0;
        double r603447 = r603445 * r603446;
        double r603448 = b;
        double r603449 = r603447 * r603448;
        double r603450 = r603444 + r603449;
        return r603450;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r603451 = y;
        double r603452 = 9.0;
        double r603453 = r603451 * r603452;
        double r603454 = z;
        double r603455 = r603453 * r603454;
        double r603456 = t;
        double r603457 = r603455 * r603456;
        double r603458 = -4.8682544554951165e+284;
        bool r603459 = r603457 <= r603458;
        double r603460 = 8.519303710692691e+306;
        bool r603461 = r603457 <= r603460;
        double r603462 = !r603461;
        bool r603463 = r603459 || r603462;
        double r603464 = 2.0;
        double r603465 = x;
        double r603466 = r603464 * r603465;
        double r603467 = r603454 * r603456;
        double r603468 = r603467 * r603453;
        double r603469 = r603466 - r603468;
        double r603470 = a;
        double r603471 = 27.0;
        double r603472 = b;
        double r603473 = r603471 * r603472;
        double r603474 = r603470 * r603473;
        double r603475 = r603469 + r603474;
        double r603476 = r603472 * r603470;
        double r603477 = r603471 * r603476;
        double r603478 = r603454 * r603451;
        double r603479 = -r603478;
        double r603480 = r603479 * r603456;
        double r603481 = r603452 * r603480;
        double r603482 = r603477 + r603481;
        double r603483 = r603466 + r603482;
        double r603484 = r603463 ? r603475 : r603483;
        return r603484;
}

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

Original3.6
Target2.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (* (* y 9.0) z) t) < -4.8682544554951165e+284 or 8.519303710692691e+306 < (* (* (* y 9.0) z) t)

    1. Initial program 55.3

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

    2. Simplified55.3

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

    4. Applied associate-*l*5.0

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

    if -4.8682544554951165e+284 < (* (* (* y 9.0) z) t) < 8.519303710692691e+306

    1. Initial program 0.5

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

    2. Simplified0.4

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

    3. Taylor expanded around inf 0.4

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

    4. Simplified0.5

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

    6. Applied sub-neg0.5

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

    7. Simplified0.4

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le -4.868254455495116538116089271342050718719 \cdot 10^{284} \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le 8.519303710692691346111528747466709815103 \cdot 10^{306}\right):\\ \;\;\;\;\left(2 \cdot x - \left(z \cdot t\right) \cdot \left(y \cdot 9\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + \left(27 \cdot \left(b \cdot a\right) + 9 \cdot \left(\left(-z \cdot y\right) \cdot t\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(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)))