Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Average Error: 7.2 → 0.4

Time: 5.3s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -9.63027742307339078 \cdot 10^{226} \lor \neg \left(x \cdot y - z \cdot y \le -5.43419999101085541 \cdot 10^{-173} \lor \neg \left(x \cdot y - z \cdot y \le 0.0 \lor \neg \left(x \cdot y - z \cdot y \le 2.8751325406658681 \cdot 10^{252}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

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)))) <= -9.63027742307339e+226) || !((((double) (((double) (x * y)) - ((double) (z * y)))) <= -5.4341999910108554e-173) || !((((double) (((double) (x * y)) - ((double) (z * y)))) <= 0.0) || !(((double) (((double) (x * y)) - ((double) (z * y)))) <= 2.875132540665868e+252))))) {
		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	7.2
Target	3.2
Herbie	0.4

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

Derivation

1. Split input into 2 regimes

2. if (- (* x y) (* z y)) < -9.63027742307339078e226 or -5.43419999101085541e-173 < (- (* x y) (* z y)) < 0.0 or 2.8751325406658681e252 < (- (* x y) (* z y))

   1. Initial program 26.1

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

   3. Applied distribute-rgt-out-- 26.1

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

   4. Applied associate-*l* 0.7

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

   if -9.63027742307339078e226 < (- (* x y) (* z y)) < -5.43419999101085541e-173 or 0.0 < (- (* x y) (* z y)) < 2.8751325406658681e252

   1. Initial program 0.3

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

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \le -9.63027742307339078 \cdot 10^{226} \lor \neg \left(x \cdot y - z \cdot y \le -5.43419999101085541 \cdot 10^{-173} \lor \neg \left(x \cdot y - z \cdot y \le 0.0 \lor \neg \left(x \cdot y - z \cdot y \le 2.8751325406658681 \cdot 10^{252}\right)\right)\right):\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot y\right) \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2020175 
(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))