Average Error: 33.4 → 0.5
Time: 4.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{z}{t}\right|}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{z}{t}\right|}
double f(double x, double y, double z, double t) {
        double r683892 = x;
        double r683893 = r683892 * r683892;
        double r683894 = y;
        double r683895 = r683894 * r683894;
        double r683896 = r683893 / r683895;
        double r683897 = z;
        double r683898 = r683897 * r683897;
        double r683899 = t;
        double r683900 = r683899 * r683899;
        double r683901 = r683898 / r683900;
        double r683902 = r683896 + r683901;
        return r683902;
}
↓
double f(double x, double y, double z, double t) {
        double r683903 = x;
        double r683904 = y;
        double r683905 = r683903 / r683904;
        double r683906 = r683905 * r683905;
        double r683907 = z;
        double r683908 = t;
        double r683909 = r683907 / r683908;
        double r683910 = fabs(r683909);
        double r683911 = 1.5;
        double r683912 = pow(r683910, r683911);
        double r683913 = sqrt(r683910);
        double r683914 = r683912 * r683913;
        double r683915 = r683906 + r683914;
        return r683915;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original33.4
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.4

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
  2. Using strategy rm

  3. Applied times-frac19.1

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt19.2

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\sqrt{\frac{z \cdot z}{t \cdot t}} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}}\]

  6. Simplified19.1

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\left|\frac{z}{t}\right|} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}\]

  7. Simplified0.4

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \left|\frac{z}{t}\right| \cdot \color{blue}{\left|\frac{z}{t}\right|}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.6

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{{\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}} \cdot \sqrt{\left|\frac{z}{t}\right|}\]
  12. Using strategy rm

  13. Applied pow1/20.6

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + {\color{blue}{\left({\left(\left|\frac{z}{t}\right|\right)}^{\frac{1}{2}}\right)}}^{3} \cdot \sqrt{\left|\frac{z}{t}\right|}\]

  14. Applied pow-pow0.5

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{{\left(\left|\frac{z}{t}\right|\right)}^{\left(\frac{1}{2} \cdot 3\right)}} \cdot \sqrt{\left|\frac{z}{t}\right|}\]

  15. Simplified0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019362 
(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))))