Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Average Error: 7.1 → 2.1

Time: 4.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t = -\infty \lor \neg \left(\left(x \cdot y - z \cdot y\right) \cdot t \le 1.26480869441227944 \cdot 10^{250}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((((((x * y) - (z * y)) * t) <= -inf.0) || !((((x * y) - (z * y)) * t) <= 1.2648086944122794e+250))) {
		VAR = (y * ((x - z) * t));
	} else {
		VAR = (((x * y) - (z * y)) * t);
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	7.1
Target	2.9
Herbie	2.1

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

Derivation

1. Split input into 2 regimes

2. if (* (- (* x y) (* z y)) t) < -inf.0 or 1.2648086944122794e+250 < (* (- (* x y) (* z y)) t)

   1. Initial program 49.1

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

   3. Applied distribute-rgt-out-- 49.1

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

   4. Applied associate-*l* 6.3

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

   if -inf.0 < (* (- (* x y) (* z y)) t) < 1.2648086944122794e+250

   1. Initial program 1.5

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

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y - z \cdot y\right) \cdot t = -\infty \lor \neg \left(\left(x \cdot y - z \cdot y\right) \cdot t \le 1.26480869441227944 \cdot 10^{250}\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020106 
(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))