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

Average Error: 3.5 → 0.8

Time: 3.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -4.8789212851081629 \cdot 10^{97}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot 3} \cdot \frac{1}{y}\\ \mathbf{elif}\;z \cdot 3 \le 9.9293498959749377 \cdot 10^{-50}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((z * 3.0) <= -4.878921285108163e+97)) {
		VAR = ((x - (y / (z * 3.0))) + ((t / (z * 3.0)) * (1.0 / y)));
	} else {
		double VAR_1;
		if (((z * 3.0) <= 9.929349895974938e-50)) {
			VAR_1 = ((x - (y / (z * 3.0))) + ((t / y) / (z * 3.0)));
		} else {
			VAR_1 = ((x - (y / (z * 3.0))) + (1.0 / (((z * 3.0) * y) / t)));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	3.5
Target	1.7
Herbie	0.8

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

Derivation

1. Split input into 3 regimes

2. if (* z 3.0) < -4.878921285108163e+97

   1. Initial program 0.5

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

   3. Applied associate-/r* 1.2

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

   5. Applied div-inv 1.2

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

   if -4.878921285108163e+97 < (* z 3.0) < 9.929349895974938e-50

   1. Initial program 8.4

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

   3. Applied associate-/r* 2.7

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

   5. Applied div-inv 2.7

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

   7. Applied associate-*l/ 1.0

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

   8. Simplified 1.0

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

   if 9.929349895974938e-50 < (* z 3.0)

   1. Initial program 0.5

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

   3. Applied clear-num 0.5

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}}\]
3. Recombined 3 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -4.8789212851081629 \cdot 10^{97}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot 3} \cdot \frac{1}{y}\\ \mathbf{elif}\;z \cdot 3 \le 9.9293498959749377 \cdot 10^{-50}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))