Average Error: 33.7 → 0.6
Time: 46.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{t}} \cdot \sqrt[3]{z}\right)\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \frac{z}{t}\right) + \frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{t}} \cdot \sqrt[3]{z}\right)\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \frac{z}{t}\right) + \frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt{\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 r28014965 = x;
        double r28014966 = r28014965 * r28014965;
        double r28014967 = y;
        double r28014968 = r28014967 * r28014967;
        double r28014969 = r28014966 / r28014968;
        double r28014970 = z;
        double r28014971 = r28014970 * r28014970;
        double r28014972 = t;
        double r28014973 = r28014972 * r28014972;
        double r28014974 = r28014971 / r28014973;
        double r28014975 = r28014969 + r28014974;
        return r28014975;
}
↓
double f(double x, double y, double z, double t) {
        double r28014976 = z;
        double r28014977 = t;
        double r28014978 = r28014976 / r28014977;
        double r28014979 = cbrt(r28014978);
        double r28014980 = 1.0;
        double r28014981 = r28014980 / r28014977;
        double r28014982 = cbrt(r28014981);
        double r28014983 = cbrt(r28014976);
        double r28014984 = r28014982 * r28014983;
        double r28014985 = r28014979 * r28014984;
        double r28014986 = r28014979 * r28014978;
        double r28014987 = r28014985 * r28014986;
        double r28014988 = x;
        double r28014989 = y;
        double r28014990 = r28014988 / r28014989;
        double r28014991 = r28014990 * r28014990;
        double r28014992 = r28014987 + r28014991;
        double r28014993 = sqrt(r28014992);
        double r28014994 = r28014978 * r28014978;
        double r28014995 = r28014991 + r28014994;
        double r28014996 = sqrt(r28014995);
        double r28014997 = r28014993 * r28014996;
        return r28014997;
}

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

Derivation

  1. Initial program 33.7

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

  2. 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-sqr-sqrt0.4

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

  6. Applied add-cube-cbrt0.6

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

  7. Applied associate-*l*0.6

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

  9. Applied div-inv0.6

    \[\leadsto \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\color{blue}{z \cdot \frac{1}{t}}}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \frac{z}{t}\right)}\]

  10. Applied cbrt-prod0.6

    \[\leadsto \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t}} \cdot \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{\frac{1}{t}}\right)}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \frac{z}{t}\right)}\]

  11. Final simplification0.6

    \[\leadsto \sqrt{\left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{t}} \cdot \sqrt[3]{z}\right)\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \frac{z}{t}\right) + \frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt{\frac{x}{y} \cdot \frac{x}{y} + \frac{z}{t} \cdot \frac{z}{t}}\]

Reproduce

herbie shell --seed 2019168 
(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))))