Average Error: 33.9 → 0.7
Time: 15.2s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\frac{z}{t} \cdot \sqrt[3]{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{z}{t}\right)}\right) \cdot \sqrt[3]{\frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \left(\frac{z}{t} \cdot \sqrt[3]{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{z}{t}\right)}\right) \cdot \sqrt[3]{\frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r43406872 = x;
        double r43406873 = r43406872 * r43406872;
        double r43406874 = y;
        double r43406875 = r43406874 * r43406874;
        double r43406876 = r43406873 / r43406875;
        double r43406877 = z;
        double r43406878 = r43406877 * r43406877;
        double r43406879 = t;
        double r43406880 = r43406879 * r43406879;
        double r43406881 = r43406878 / r43406880;
        double r43406882 = r43406876 + r43406881;
        return r43406882;
}
↓
double f(double x, double y, double z, double t) {
        double r43406883 = x;
        double r43406884 = y;
        double r43406885 = r43406883 / r43406884;
        double r43406886 = r43406885 * r43406885;
        double r43406887 = z;
        double r43406888 = t;
        double r43406889 = r43406887 / r43406888;
        double r43406890 = cbrt(r43406887);
        double r43406891 = r43406890 * r43406890;
        double r43406892 = cbrt(r43406888);
        double r43406893 = r43406892 * r43406892;
        double r43406894 = r43406891 / r43406893;
        double r43406895 = r43406890 / r43406892;
        double r43406896 = r43406895 * r43406889;
        double r43406897 = r43406894 * r43406896;
        double r43406898 = cbrt(r43406897);
        double r43406899 = r43406889 * r43406898;
        double r43406900 = cbrt(r43406889);
        double r43406901 = r43406899 * r43406900;
        double r43406902 = r43406886 + r43406901;
        return r43406902;
}

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

Original33.9
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.9

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

  2. 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

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

  5. Applied associate-*r*0.8

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

  7. Applied cbrt-unprod0.6

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

  9. Applied add-cube-cbrt0.7

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

  10. Applied add-cube-cbrt0.7

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

  11. Applied times-frac0.7

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

  12. Applied associate-*l*0.7

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

  13. Final simplification0.7

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

Reproduce

herbie shell --seed 2019174 
(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))))