Average Error: 3.5 → 0.9
Time: 12.4s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.660311807137084788107015105621119988366 \cdot 10^{90} \lor \neg \left(t \le 6.858672798378862507206508113638693409984 \cdot 10^{53}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \end{array}\]
\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}\;t \le -6.660311807137084788107015105621119988366 \cdot 10^{90} \lor \neg \left(t \le 6.858672798378862507206508113638693409984 \cdot 10^{53}\right):\\
\;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1233537 = x;
        double r1233538 = 2.0;
        double r1233539 = r1233537 * r1233538;
        double r1233540 = y;
        double r1233541 = 9.0;
        double r1233542 = r1233540 * r1233541;
        double r1233543 = z;
        double r1233544 = r1233542 * r1233543;
        double r1233545 = t;
        double r1233546 = r1233544 * r1233545;
        double r1233547 = r1233539 - r1233546;
        double r1233548 = a;
        double r1233549 = 27.0;
        double r1233550 = r1233548 * r1233549;
        double r1233551 = b;
        double r1233552 = r1233550 * r1233551;
        double r1233553 = r1233547 + r1233552;
        return r1233553;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1233554 = t;
        double r1233555 = -6.660311807137085e+90;
        bool r1233556 = r1233554 <= r1233555;
        double r1233557 = 6.8586727983788625e+53;
        bool r1233558 = r1233554 <= r1233557;
        double r1233559 = !r1233558;
        bool r1233560 = r1233556 || r1233559;
        double r1233561 = x;
        double r1233562 = 2.0;
        double r1233563 = r1233561 * r1233562;
        double r1233564 = y;
        double r1233565 = 9.0;
        double r1233566 = r1233564 * r1233565;
        double r1233567 = z;
        double r1233568 = r1233566 * r1233567;
        double r1233569 = r1233568 * r1233554;
        double r1233570 = r1233563 - r1233569;
        double r1233571 = 27.0;
        double r1233572 = a;
        double r1233573 = b;
        double r1233574 = r1233572 * r1233573;
        double r1233575 = r1233571 * r1233574;
        double r1233576 = r1233570 + r1233575;
        double r1233577 = r1233567 * r1233554;
        double r1233578 = r1233566 * r1233577;
        double r1233579 = r1233563 - r1233578;
        double r1233580 = r1233571 * r1233573;
        double r1233581 = r1233572 * r1233580;
        double r1233582 = r1233579 + r1233581;
        double r1233583 = r1233560 ? r1233576 : r1233582;
        return r1233583;
}

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

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

Derivation

  1. Split input into 2 regimes

  2. if t < -6.660311807137085e+90 or 6.8586727983788625e+53 < t

    1. Initial program 0.8

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

    2. Taylor expanded around 0 0.8

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

    if -6.660311807137085e+90 < t < 6.8586727983788625e+53

    1. Initial program 4.7

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

    3. Applied associate-*l*4.7

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

    5. Applied associate-*l*1.0

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.660311807137084788107015105621119988366 \cdot 10^{90} \lor \neg \left(t \le 6.858672798378862507206508113638693409984 \cdot 10^{53}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b)))

  (+ (- (* x 2) (* (* (* y 9) z) t)) (* (* a 27) b)))