Average Error: 4.1 → 1.4
Time: 13.6s
Precision: binary64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.1157888557815517 \cdot 10^{89}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;t \le 3.57534701269823601 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \le 1.9695046733778307 \cdot 10^{243}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - \left(\left(9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array}\]
\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 -1.1157888557815517 \cdot 10^{89}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{elif}\;t \le 3.57534701269823601 \cdot 10^{-38}:\\
\;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\

\mathbf{elif}\;t \le 1.9695046733778307 \cdot 10^{243}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\

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

\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 ((t <= -1.1157888557815517e+89)) {
		VAR = ((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (y * ((double) (9.0 * z)))) * t)))) + ((double) (((double) (a * 27.0)) * b))));
	} else {
		double VAR_1;
		if ((t <= 3.575347012698236e-38)) {
			VAR_1 = ((double) (((double) (x * 2.0)) + ((double) (((double) (27.0 * ((double) (a * b)))) - ((double) (((double) (y * 9.0)) * ((double) (z * t))))))));
		} else {
			double VAR_2;
			if ((t <= 1.9695046733778307e+243)) {
				VAR_2 = ((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (y * ((double) (9.0 * z)))) * t)))) + ((double) (((double) (a * 27.0)) * b))));
			} else {
				VAR_2 = ((double) (((double) (((double) (2.0 * x)) + ((double) (27.0 * ((double) (a * b)))))) - ((double) (((double) (((double) (9.0 * t)) * z)) * y))));
			}
			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

Original4.1
Target2.6
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 t < -1.1157888557815517e89 or 3.57534701269823601e-38 < t < 1.9695046733778307e243

    1. Initial program 1.0

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

    3. Applied associate-*l*0.9

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

    if -1.1157888557815517e89 < t < 3.57534701269823601e-38

    1. Initial program 5.8

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

    3. Applied sub-neg5.8

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

    4. Applied associate-+l+5.8

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

    5. Simplified5.7

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

    7. Applied associate-*l*0.9

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

    if 1.9695046733778307e243 < t

    1. Initial program 3.1

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

    3. Applied sub-neg3.1

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

    4. Applied associate-+l+3.1

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

    5. Simplified2.9

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

    6. Taylor expanded around inf 2.9

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

    8. Applied associate-*r*3.6

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

    10. Applied associate-*r*15.3

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.1157888557815517 \cdot 10^{89}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;t \le 3.57534701269823601 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;t \le 1.9695046733778307 \cdot 10^{243}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - \left(\left(9 \cdot t\right) \cdot z\right) \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020164 
(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)))