Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1

Average Error: 33.9 → 0.5

Time: 11.7s

Precision: 64

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

Math

\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

↓

\[\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \left(\sqrt{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}} \cdot \sqrt{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}}\right) \cdot \sqrt{\left|\frac{z}{t}\right|}\right)\]

C

double f(double x, double y, double z, double t) {
        double r697985 = x;
        double r697986 = r697985 * r697985;
        double r697987 = y;
        double r697988 = r697987 * r697987;
        double r697989 = r697986 / r697988;
        double r697990 = z;
        double r697991 = r697990 * r697990;
        double r697992 = t;
        double r697993 = r697992 * r697992;
        double r697994 = r697991 / r697993;
        double r697995 = r697989 + r697994;
        return r697995;
}

↓

double f(double x, double y, double z, double t) {
        double r697996 = x;
        double r697997 = y;
        double r697998 = r697996 / r697997;
        double r697999 = z;
        double r698000 = t;
        double r698001 = r697999 / r698000;
        double r698002 = fabs(r698001);
        double r698003 = 1.5;
        double r698004 = pow(r698002, r698003);
        double r698005 = sqrt(r698004);
        double r698006 = r698005 * r698005;
        double r698007 = sqrt(r698002);
        double r698008 = r698006 * r698007;
        double r698009 = fma(r697998, r697998, r698008);
        return r698009;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	33.9
Target	0.4
Herbie	0.5

\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

1. Initial program 33.9

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

2. Simplified 19.3

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \frac{z \cdot z}{t \cdot t}\right)}\]
3. Using strategy rm

4. Applied add-sqr-sqrt 19.4

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \color{blue}{\sqrt{\frac{z \cdot z}{t \cdot t}} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}}\right)\]

5. Simplified 19.3

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \color{blue}{\left|\frac{z}{t}\right|} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}\right)\]

6. Simplified 0.4

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \left|\frac{z}{t}\right| \cdot \color{blue}{\left|\frac{z}{t}\right|}\right)\]
7. Using strategy rm

8. Applied add-sqr-sqrt 0.5

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \left|\frac{z}{t}\right| \cdot \color{blue}{\left(\sqrt{\left|\frac{z}{t}\right|} \cdot \sqrt{\left|\frac{z}{t}\right|}\right)}\right)\]

9. Applied associate-*r* 0.5

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \color{blue}{\left(\left|\frac{z}{t}\right| \cdot \sqrt{\left|\frac{z}{t}\right|}\right) \cdot \sqrt{\left|\frac{z}{t}\right|}}\right)\]

10. Simplified 0.5

    \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \color{blue}{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}} \cdot \sqrt{\left|\frac{z}{t}\right|}\right)\]
11. Using strategy rm

12. Applied add-sqr-sqrt 0.5

    \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \color{blue}{\left(\sqrt{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}} \cdot \sqrt{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}}\right)} \cdot \sqrt{\left|\frac{z}{t}\right|}\right)\]

13. Final simplification 0.5

    \[\leadsto \mathsf{fma}\left(\frac{x}{y}, \frac{x}{y}, \left(\sqrt{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}} \cdot \sqrt{{\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}}\right) \cdot \sqrt{\left|\frac{z}{t}\right|}\right)\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

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