Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3

Average Error: 10.1 → 0.5

Time: 15.3s

Precision: 64

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

Math

\[\frac{x + y \cdot \left(z - x\right)}{z}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -45420229474314215424 \lor \neg \left(z \le 1.362460892796714133568053707648303694307 \cdot 10^{-154}\right):\\ \;\;\;\;\left(\frac{x}{z} + y\right) - \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{z} + y\right) - \frac{x \cdot y}{z}\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r996783 = x;
        double r996784 = y;
        double r996785 = z;
        double r996786 = r996785 - r996783;
        double r996787 = r996784 * r996786;
        double r996788 = r996783 + r996787;
        double r996789 = r996788 / r996785;
        return r996789;
}

↓

double f(double x, double y, double z) {
        double r996790 = z;
        double r996791 = -4.5420229474314215e+19;
        bool r996792 = r996790 <= r996791;
        double r996793 = 1.3624608927967141e-154;
        bool r996794 = r996790 <= r996793;
        double r996795 = !r996794;
        bool r996796 = r996792 || r996795;
        double r996797 = x;
        double r996798 = r996797 / r996790;
        double r996799 = y;
        double r996800 = r996798 + r996799;
        double r996801 = r996790 / r996799;
        double r996802 = r996797 / r996801;
        double r996803 = r996800 - r996802;
        double r996804 = r996797 * r996799;
        double r996805 = r996804 / r996790;
        double r996806 = r996800 - r996805;
        double r996807 = r996796 ? r996803 : r996806;
        return r996807;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	10.1
Target	0.0
Herbie	0.5

\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

1. Split input into 2 regimes

2. if z < -4.5420229474314215e+19 or 1.3624608927967141e-154 < z

   1. Initial program 14.4

      \[\frac{x + y \cdot \left(z - x\right)}{z}\]

   2. Taylor expanded around 0 5.1

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

   4. Applied associate-/l* 0.7

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

   if -4.5420229474314215e+19 < z < 1.3624608927967141e-154

   1. Initial program 0.1

      \[\frac{x + y \cdot \left(z - x\right)}{z}\]

   2. Taylor expanded around 0 0.1

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

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -45420229474314215424 \lor \neg \left(z \le 1.362460892796714133568053707648303694307 \cdot 10^{-154}\right):\\ \;\;\;\;\left(\frac{x}{z} + y\right) - \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{z} + y\right) - \frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))