Average Error: 33.7 → 0.8
Time: 13.7s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r444870 = x;
        double r444871 = r444870 * r444870;
        double r444872 = y;
        double r444873 = r444872 * r444872;
        double r444874 = r444871 / r444873;
        double r444875 = z;
        double r444876 = r444875 * r444875;
        double r444877 = t;
        double r444878 = r444877 * r444877;
        double r444879 = r444876 / r444878;
        double r444880 = r444874 + r444879;
        return r444880;
}
↓
double f(double x, double y, double z, double t) {
        double r444881 = x;
        double r444882 = y;
        double r444883 = r444881 / r444882;
        double r444884 = r444883 * r444883;
        double r444885 = z;
        double r444886 = t;
        double r444887 = r444885 / r444886;
        double r444888 = r444887 * r444887;
        double r444889 = cbrt(r444888);
        double r444890 = r444889 * r444889;
        double r444891 = r444890 * r444889;
        double r444892 = r444884 + r444891;
        return r444892;
}

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

Original33.7
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

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 times-frac19.2

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

  5. Applied times-frac0.4

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

  7. Applied add-cube-cbrt0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019325 
(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))))