Average Error: 33.8 → 0.6
Time: 5.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \left(\frac{z}{t} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right)\right) \cdot \sqrt[3]{\frac{z}{t}}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt{\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \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}}}
double f(double x, double y, double z, double t) {
        double r774844 = x;
        double r774845 = r774844 * r774844;
        double r774846 = y;
        double r774847 = r774846 * r774846;
        double r774848 = r774845 / r774847;
        double r774849 = z;
        double r774850 = r774849 * r774849;
        double r774851 = t;
        double r774852 = r774851 * r774851;
        double r774853 = r774850 / r774852;
        double r774854 = r774848 + r774853;
        return r774854;
}
↓
double f(double x, double y, double z, double t) {
        double r774855 = x;
        double r774856 = y;
        double r774857 = r774855 / r774856;
        double r774858 = fabs(r774857);
        double r774859 = r774858 * r774858;
        double r774860 = z;
        double r774861 = t;
        double r774862 = r774860 / r774861;
        double r774863 = r774862 * r774862;
        double r774864 = r774859 + r774863;
        double r774865 = sqrt(r774864);
        double r774866 = cbrt(r774862);
        double r774867 = r774866 * r774866;
        double r774868 = r774862 * r774867;
        double r774869 = r774868 * r774866;
        double r774870 = r774859 + r774869;
        double r774871 = sqrt(r774870);
        double r774872 = r774865 * r774871;
        return r774872;
}

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

Original33.8
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.8

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
  2. Using strategy rm

  3. Applied times-frac20.0

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

  5. Applied add-sqr-sqrt20.1

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

  6. Simplified20.0

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

  7. Simplified0.4

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

  9. Applied add-sqr-sqrt0.4

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

  11. Applied add-cube-cbrt0.6

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

  12. Applied associate-*r*0.6

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

  13. Final simplification0.6

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

Reproduce

herbie shell --seed 2020089 
(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))))