Average Error: 33.7 → 0.6
Time: 4.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r632879 = x;
        double r632880 = r632879 * r632879;
        double r632881 = y;
        double r632882 = r632881 * r632881;
        double r632883 = r632880 / r632882;
        double r632884 = z;
        double r632885 = r632884 * r632884;
        double r632886 = t;
        double r632887 = r632886 * r632886;
        double r632888 = r632885 / r632887;
        double r632889 = r632883 + r632888;
        return r632889;
}
↓
double f(double x, double y, double z, double t) {
        double r632890 = x;
        double r632891 = y;
        double r632892 = r632890 / r632891;
        double r632893 = fabs(r632892);
        double r632894 = sqrt(r632893);
        double r632895 = 3.0;
        double r632896 = pow(r632894, r632895);
        double r632897 = r632894 * r632896;
        double r632898 = z;
        double r632899 = t;
        double r632900 = r632898 / r632899;
        double r632901 = r632900 * r632900;
        double r632902 = r632897 + r632901;
        return r632902;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original33.7
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.7

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

  3. Applied add-sqr-sqrt33.7

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

  4. Simplified33.7

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

  5. Simplified19.1

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

  7. Applied times-frac0.4

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

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2020001 
(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))))