Average Error: 33.7 → 0.8
Time: 4.6s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r685977 = x;
        double r685978 = r685977 * r685977;
        double r685979 = y;
        double r685980 = r685979 * r685979;
        double r685981 = r685978 / r685980;
        double r685982 = z;
        double r685983 = r685982 * r685982;
        double r685984 = t;
        double r685985 = r685984 * r685984;
        double r685986 = r685983 / r685985;
        double r685987 = r685981 + r685986;
        return r685987;
}
↓
double f(double x, double y, double z, double t) {
        double r685988 = x;
        double r685989 = y;
        double r685990 = r685988 / r685989;
        double r685991 = r685990 * r685990;
        double r685992 = cbrt(r685991);
        double r685993 = r685992 * r685992;
        double r685994 = r685993 * r685992;
        double r685995 = z;
        double r685996 = t;
        double r685997 = r685995 / r685996;
        double r685998 = r685997 * r685997;
        double r685999 = r685994 + r685998;
        return r685999;
}

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-frac19.1

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

  5. Applied times-frac0.4

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

  7. Applied add-cube-cbrt0.8

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

  8. Final simplification0.8

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

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))))