Average Error: 33.4 → 0.7
Time: 20.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \left(\sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}} \cdot \sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \frac{x}{y}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \left(\sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}} \cdot \sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r27915874 = x;
        double r27915875 = r27915874 * r27915874;
        double r27915876 = y;
        double r27915877 = r27915876 * r27915876;
        double r27915878 = r27915875 / r27915877;
        double r27915879 = z;
        double r27915880 = r27915879 * r27915879;
        double r27915881 = t;
        double r27915882 = r27915881 * r27915881;
        double r27915883 = r27915880 / r27915882;
        double r27915884 = r27915878 + r27915883;
        return r27915884;
}
↓
double f(double x, double y, double z, double t) {
        double r27915885 = z;
        double r27915886 = t;
        double r27915887 = r27915885 / r27915886;
        double r27915888 = r27915887 * r27915887;
        double r27915889 = x;
        double r27915890 = y;
        double r27915891 = r27915889 / r27915890;
        double r27915892 = r27915891 * r27915891;
        double r27915893 = cbrt(r27915892);
        double r27915894 = sqrt(r27915893);
        double r27915895 = r27915894 * r27915894;
        double r27915896 = cbrt(r27915891);
        double r27915897 = r27915896 * r27915891;
        double r27915898 = r27915895 * r27915897;
        double r27915899 = r27915888 + r27915898;
        return r27915899;
}

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

Derivation

  1. Initial program 33.4

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

  2. Simplified0.4

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

  4. Applied add-cube-cbrt0.8

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

  5. Applied associate-*l*0.8

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

  7. Applied cbrt-unprod0.6

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

  9. Applied add-sqr-sqrt0.7

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

  10. Final simplification0.7

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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