Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Average Error: 3.7 → 0.6

Time: 4.4s

Precision: binary64

Math

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]

↓

\[\begin{array}{l} \mathbf{if}\;t \le -1.1603011515056161 \cdot 10^{63}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\left(y \cdot z\right) \cdot \frac{3}{t}}\\ \mathbf{elif}\;t \le 5.9811512974853166 \cdot 10^{88}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array}\]

C

double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (t / ((double) (((double) (z * 3.0)) * y))))));
}

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((t <= -1.1603011515056161e+63)) {
		VAR = ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (1.0 / ((double) (((double) (y * z)) * ((double) (3.0 / t))))))));
	} else {
		double VAR_1;
		if ((t <= 5.9811512974853166e+88)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (t / y)) - y)) / ((double) (z * 3.0))))));
		} else {
			VAR_1 = ((double) (((double) (x - ((double) (((double) (y / z)) / 3.0)))) + ((double) (t / ((double) (y * ((double) (z * 3.0))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	3.7
Target	1.9
Herbie	0.6

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

1. Split input into 3 regimes

2. if t < -1.1603011515056161e63

   1. Initial program 0.6

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
   2. Using strategy rm

   3. Applied clear-num 0.6

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}}\]

   4. Simplified 0.6

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\color{blue}{\frac{z \cdot y}{t} \cdot 3}}\]
   5. Using strategy rm

   6. Applied clear-num 0.6

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{\frac{\frac{z \cdot y}{t} \cdot 3}{1}}}\]

   7. Simplified 0.6

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\color{blue}{\left(z \cdot y\right) \cdot \frac{3}{t}}}\]

   if -1.1603011515056161e63 < t < 5.9811512974853166e88

   1. Initial program 5.1

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]

   2. Simplified 0.6

      \[\leadsto \color{blue}{x + \frac{\frac{t}{y} - y}{z \cdot 3}}\]

   if 5.9811512974853166e88 < t

   1. Initial program 0.6

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
   2. Using strategy rm

   3. Applied associate-/r* 0.6

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.1603011515056161 \cdot 10^{63}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\left(y \cdot z\right) \cdot \frac{3}{t}}\\ \mathbf{elif}\;t \le 5.9811512974853166 \cdot 10^{88}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))