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

Average Error: 33.9 → 0.9

Time: 12.5s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r687967 = x;
        double r687968 = r687967 * r687967;
        double r687969 = y;
        double r687970 = r687969 * r687969;
        double r687971 = r687968 / r687970;
        double r687972 = z;
        double r687973 = r687972 * r687972;
        double r687974 = t;
        double r687975 = r687974 * r687974;
        double r687976 = r687973 / r687975;
        double r687977 = r687971 + r687976;
        return r687977;
}

↓

double f(double x, double y, double z, double t) {
        double r687978 = x;
        double r687979 = y;
        double r687980 = r687978 / r687979;
        double r687981 = z;
        double r687982 = t;
        double r687983 = r687981 / r687982;
        double r687984 = cbrt(r687981);
        double r687985 = r687984 * r687984;
        double r687986 = cbrt(r687982);
        double r687987 = r687986 * r687986;
        double r687988 = r687985 / r687987;
        double r687989 = r687983 * r687988;
        double r687990 = r687984 / r687986;
        double r687991 = r687989 * r687990;
        double r687992 = fma(r687980, r687980, r687991);
        return r687992;
}

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	0.9

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

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 times-frac 0.4

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

6. Applied add-cube-cbrt 0.8

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

7. Applied add-cube-cbrt 0.9

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

8. Applied times-frac 0.9

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

9. Applied associate-*r* 0.9

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

10. Final simplification 0.9

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

Reproduce

herbie shell --seed 2020042 +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))))