Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Average Error: 6.9 → 0.6

Time: 2.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y = -\infty \lor \neg \left(x \cdot y - z \cdot y \le -1.22339818893361066 \cdot 10^{-245} \lor \neg \left(x \cdot y - z \cdot y \le 9.38092306052079621 \cdot 10^{-237} \lor \neg \left(x \cdot y - z \cdot y \le 2.32936053843261313 \cdot 10^{168}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((((x * y) - (z * y)) <= -inf.0) || !((((x * y) - (z * y)) <= -1.2233981889336107e-245) || !((((x * y) - (z * y)) <= 9.380923060520796e-237) || !(((x * y) - (z * y)) <= 2.329360538432613e+168))))) {
		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	6.9
Target	3.3
Herbie	0.6

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

Derivation

1. Split input into 2 regimes

2. if (- (* x y) (* z y)) < -inf.0 or -1.2233981889336107e-245 < (- (* x y) (* z y)) < 9.380923060520796e-237 or 2.329360538432613e+168 < (- (* x y) (* z y))

   1. Initial program 24.9

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

   3. Applied distribute-rgt-out-- 24.9

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

   4. Applied associate-*l* 1.4

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

   if -inf.0 < (- (* x y) (* z y)) < -1.2233981889336107e-245 or 9.380923060520796e-237 < (- (* x y) (* z y)) < 2.329360538432613e+168

   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 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y = -\infty \lor \neg \left(x \cdot y - z \cdot y \le -1.22339818893361066 \cdot 10^{-245} \lor \neg \left(x \cdot y - z \cdot y \le 9.38092306052079621 \cdot 10^{-237} \lor \neg \left(x \cdot y - z \cdot y \le 2.32936053843261313 \cdot 10^{168}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 +o rules:numerics
(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))