Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Average Error: 2.1 → 0.3

Time: 18.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -28307743179575658671131851877253120:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \mathbf{elif}\;b \le 64832796670992064512:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + \left(z \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r36565636 = x;
        double r36565637 = y;
        double r36565638 = z;
        double r36565639 = r36565637 * r36565638;
        double r36565640 = r36565636 + r36565639;
        double r36565641 = t;
        double r36565642 = a;
        double r36565643 = r36565641 * r36565642;
        double r36565644 = r36565640 + r36565643;
        double r36565645 = r36565642 * r36565638;
        double r36565646 = b;
        double r36565647 = r36565645 * r36565646;
        double r36565648 = r36565644 + r36565647;
        return r36565648;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r36565649 = b;
        double r36565650 = -2.830774317957566e+34;
        bool r36565651 = r36565649 <= r36565650;
        double r36565652 = a;
        double r36565653 = z;
        double r36565654 = r36565652 * r36565653;
        double r36565655 = r36565654 * r36565649;
        double r36565656 = x;
        double r36565657 = y;
        double r36565658 = r36565657 * r36565653;
        double r36565659 = r36565656 + r36565658;
        double r36565660 = t;
        double r36565661 = r36565652 * r36565660;
        double r36565662 = r36565659 + r36565661;
        double r36565663 = r36565655 + r36565662;
        double r36565664 = 6.4832796670992065e+19;
        bool r36565665 = r36565649 <= r36565664;
        double r36565666 = r36565653 * r36565649;
        double r36565667 = r36565666 * r36565652;
        double r36565668 = r36565662 + r36565667;
        double r36565669 = r36565665 ? r36565668 : r36565663;
        double r36565670 = r36565651 ? r36565663 : r36565669;
        return r36565670;
}

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	2.1
Target	0.5
Herbie	0.3

\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if b < -2.830774317957566e+34 or 6.4832796670992065e+19 < b

   1. Initial program 0.6

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

   if -2.830774317957566e+34 < b < 6.4832796670992065e+19

   1. Initial program 3.1

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

   3. Applied associate-*l* 0.1

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

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -28307743179575658671131851877253120:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \mathbf{elif}\;b \le 64832796670992064512:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + a \cdot t\right) + \left(z \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"

  :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)))