Average Error: 33.7 → 0.7
Time: 5.6s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \sqrt[3]{{\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \sqrt[3]{{\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}} \cdot {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3}
double f(double x, double y, double z, double t) {
        double r742971 = x;
        double r742972 = r742971 * r742971;
        double r742973 = y;
        double r742974 = r742973 * r742973;
        double r742975 = r742972 / r742974;
        double r742976 = z;
        double r742977 = r742976 * r742976;
        double r742978 = t;
        double r742979 = r742978 * r742978;
        double r742980 = r742977 / r742979;
        double r742981 = r742975 + r742980;
        return r742981;
}
↓
double f(double x, double y, double z, double t) {
        double r742982 = x;
        double r742983 = y;
        double r742984 = r742982 / r742983;
        double r742985 = r742984 * r742984;
        double r742986 = z;
        double r742987 = t;
        double r742988 = r742986 / r742987;
        double r742989 = fabs(r742988);
        double r742990 = sqrt(r742989);
        double r742991 = 3.0;
        double r742992 = pow(r742990, r742991);
        double r742993 = cbrt(r742992);
        double r742994 = r742993 * r742992;
        double r742995 = r742985 + r742994;
        return r742995;
}

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

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-frac18.9

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

  5. Applied add-sqr-sqrt18.9

    \[\leadsto \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\sqrt{\frac{z \cdot z}{t \cdot t}} \cdot \sqrt{\frac{z \cdot z}{t \cdot t}}}\]

  6. Simplified18.9

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

  7. Simplified0.4

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

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.6

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

  13. Applied add-cbrt-cube0.7

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

  14. Simplified0.7

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

  15. Final simplification0.7

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

Reproduce

herbie shell --seed 2020046 
(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))))