Average Error: 3.9 → 1.4
Time: 4.4s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -45596053.2280811742:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;y \cdot 9 \le 2.12866497905581898 \cdot 10^{120}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \mathbf{elif}\;y \cdot 9 \le 5.35775708626193387 \cdot 10^{216}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array}\]
\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}\;y \cdot 9 \le -45596053.2280811742:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{elif}\;y \cdot 9 \le 2.12866497905581898 \cdot 10^{120}:\\
\;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\

\mathbf{elif}\;y \cdot 9 \le 5.35775708626193387 \cdot 10^{216}:\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\

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

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (((double) (y * 9.0)) * z)) * t)))) + ((double) (((double) (a * 27.0)) * b))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if ((((double) (y * 9.0)) <= -45596053.228081174)) {
		VAR = ((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (y * 9.0)) * ((double) (z * t)))))) + ((double) (((double) (a * 27.0)) * b))));
	} else {
		double VAR_1;
		if ((((double) (y * 9.0)) <= 2.128664979055819e+120)) {
			VAR_1 = ((double) (((double) (x * 2.0)) + ((double) (((double) (27.0 * ((double) (a * b)))) - ((double) (((double) (((double) (y * 9.0)) * z)) * t))))));
		} else {
			double VAR_2;
			if ((((double) (y * 9.0)) <= 5.357757086261934e+216)) {
				VAR_2 = ((double) (((double) (((double) (x * 2.0)) - ((double) (y * ((double) (((double) sqrt(9.0)) * ((double) (((double) sqrt(9.0)) * ((double) (z * t)))))))))) + ((double) (((double) (a * 27.0)) * b))));
			} else {
				VAR_2 = ((double) (((double) (x * 2.0)) + ((double) (((double) (27.0 * ((double) (a * b)))) - ((double) (((double) (((double) (y * 9.0)) * z)) * t))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original3.9
Target2.8
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y 9.0) < -45596053.228081174

    1. Initial program 9.3

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

    3. Applied associate-*l*0.7

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

    if -45596053.228081174 < (* y 9.0) < 2.128664979055819e+120 or 5.357757086261934e+216 < (* y 9.0)

    1. Initial program 1.7

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

    3. Applied sub-neg1.7

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

    4. Applied associate-+l+1.7

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

    5. Simplified1.7

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

    if 2.128664979055819e+120 < (* y 9.0) < 5.357757086261934e+216

    1. Initial program 9.9

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

    3. Applied associate-*l*0.7

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

    5. Applied associate-*l*0.7

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

    7. Applied add-sqr-sqrt0.7

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

    8. Applied associate-*l*0.7

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -45596053.2280811742:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;y \cdot 9 \le 2.12866497905581898 \cdot 10^{120}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \mathbf{elif}\;y \cdot 9 \le 5.35775708626193387 \cdot 10^{216}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020140 
(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 2.0) (* (* (* 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)))