Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Average Error: 7.4 → 0.3

Time: 4.9s

Precision: binary64

Math

\[\left(x \cdot y - z \cdot y\right) \cdot t\]

↓

\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -5.75123028275825946 \cdot 10^{227} \lor \neg \left(x \cdot y - z \cdot y \le -7.7460261502711986 \cdot 10^{-291} \lor \neg \left(x \cdot y - z \cdot y \le 1.1672069537444567 \cdot 10^{-307} \lor \neg \left(x \cdot y - z \cdot y \le 1.13071311800251929 \cdot 10^{308}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (((double) (x * y)) - ((double) (z * y)))) <= -5.7512302827582595e+227) || !((((double) (((double) (x * y)) - ((double) (z * y)))) <= -7.746026150271199e-291) || !((((double) (((double) (x * y)) - ((double) (z * y)))) <= 1.1672069537444567e-307) || !(((double) (((double) (x * y)) - ((double) (z * y)))) <= 1.1307131180025193e+308))))) {
		VAR = ((double) (y * ((double) (((double) (x - z)) * t))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) - ((double) (z * y)))) * t));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.4
Target	3.0
Herbie	0.3

\[\begin{array}{l} \mathbf{if}\;t \lt -9.2318795828867769 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t \lt 2.5430670515648771 \cdot 10^{83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (- (* x y) (* z y)) < -5.75123028275825946e227 or -7.7460261502711986e-291 < (- (* x y) (* z y)) < 1.1672069537444567e-307 or 1.13071311800251929e308 < (- (* x y) (* z y))

   1. Initial program 36.2

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
   2. Using strategy rm

   3. Applied distribute-rgt-out-- 36.2

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

   4. Applied associate-*l* 0.6

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

   if -5.75123028275825946e227 < (- (* x y) (* z y)) < -7.7460261502711986e-291 or 1.1672069537444567e-307 < (- (* x y) (* z y)) < 1.13071311800251929e308

   1. Initial program 0.2

      \[\left(x \cdot y - z \cdot y\right) \cdot t\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -5.75123028275825946 \cdot 10^{227} \lor \neg \left(x \cdot y - z \cdot y \le -7.7460261502711986 \cdot 10^{-291} \lor \neg \left(x \cdot y - z \cdot y \le 1.1672069537444567 \cdot 10^{-307} \lor \neg \left(x \cdot y - z \cdot y \le 1.13071311800251929 \cdot 10^{308}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020174 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

  (* (- (* x y) (* z y)) t))