Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Average Error: 2.0 → 0.5

Time: 8.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 1.88966937591901725 \cdot 10^{279}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r368635 = x;
        double r368636 = y;
        double r368637 = z;
        double r368638 = r368636 * r368637;
        double r368639 = r368635 + r368638;
        double r368640 = t;
        double r368641 = a;
        double r368642 = r368640 * r368641;
        double r368643 = r368639 + r368642;
        double r368644 = r368641 * r368637;
        double r368645 = b;
        double r368646 = r368644 * r368645;
        double r368647 = r368643 + r368646;
        return r368647;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r368648 = x;
        double r368649 = y;
        double r368650 = z;
        double r368651 = r368649 * r368650;
        double r368652 = r368648 + r368651;
        double r368653 = t;
        double r368654 = a;
        double r368655 = r368653 * r368654;
        double r368656 = r368652 + r368655;
        double r368657 = r368654 * r368650;
        double r368658 = b;
        double r368659 = r368657 * r368658;
        double r368660 = r368656 + r368659;
        double r368661 = -inf.0;
        bool r368662 = r368660 <= r368661;
        double r368663 = 1.8896693759190173e+279;
        bool r368664 = r368660 <= r368663;
        double r368665 = !r368664;
        bool r368666 = r368662 || r368665;
        double r368667 = r368650 * r368658;
        double r368668 = r368654 * r368667;
        double r368669 = r368656 + r368668;
        double r368670 = r368666 ? r368669 : r368660;
        return r368670;
}

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	2.0
Target	0.4
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < -inf.0 or 1.8896693759190173e+279 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))

   1. Initial program 22.5

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

   3. Applied associate-*l* 3.9

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

   if -inf.0 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < 1.8896693759190173e+279

   1. Initial program 0.2

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

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 1.88966937591901725 \cdot 10^{279}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000) (+ (* 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)))