Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Average Error: 2.2 → 1.0

Time: 4.3s

Precision: 64

Math

\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le -2.0191618795468348 \cdot 10^{295} \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 3.6199728632000966 \cdot 10^{226}\right):\\ \;\;\;\;y \cdot z + \left(x + \left(a \cdot t + a \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b))));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if (((((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b)))) <= -2.0191618795468348e+295) || !(((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b)))) <= 3.6199728632000966e+226))) {
		VAR = ((double) (((double) (y * z)) + ((double) (x + ((double) (((double) (a * t)) + ((double) (a * ((double) (z * b))))))))));
	} else {
		VAR = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Target

Original	2.2
Target	0.3
Herbie	1.0

\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < -2.0191618795468348e+295 or 3.6199728632000966e+226 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))

   1. Initial program 9.6

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]

   2. Simplified 3.7

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

   4. Applied distribute-lft-in 3.7

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

   if -2.0191618795468348e+295 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < 3.6199728632000966e+226

   1. Initial program 0.4

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

4. Final simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le -2.0191618795468348 \cdot 10^{295} \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 3.6199728632000966 \cdot 10^{226}\right):\\ \;\;\;\;y \cdot z + \left(x + \left(a \cdot t + a \cdot \left(z \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020140 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -1.1820553527347888e+19) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))