Average Error: 34.0 → 0.7
Time: 4.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\frac{z}{t} \cdot \left(\left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{\frac{1}{t}}\right)\right) \cdot \sqrt[3]{\frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \left(\frac{z}{t} \cdot \left(\left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{\frac{1}{t}}\right)\right) \cdot \sqrt[3]{\frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r585916 = x;
        double r585917 = r585916 * r585916;
        double r585918 = y;
        double r585919 = r585918 * r585918;
        double r585920 = r585917 / r585919;
        double r585921 = z;
        double r585922 = r585921 * r585921;
        double r585923 = t;
        double r585924 = r585923 * r585923;
        double r585925 = r585922 / r585924;
        double r585926 = r585920 + r585925;
        return r585926;
}
↓
double f(double x, double y, double z, double t) {
        double r585927 = x;
        double r585928 = y;
        double r585929 = r585927 / r585928;
        double r585930 = r585929 * r585929;
        double r585931 = z;
        double r585932 = t;
        double r585933 = r585931 / r585932;
        double r585934 = cbrt(r585933);
        double r585935 = cbrt(r585931);
        double r585936 = r585934 * r585935;
        double r585937 = 1.0;
        double r585938 = r585937 / r585932;
        double r585939 = cbrt(r585938);
        double r585940 = r585936 * r585939;
        double r585941 = r585933 * r585940;
        double r585942 = r585941 * r585934;
        double r585943 = r585930 + r585942;
        return r585943;
}

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

Original34.0
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 34.0

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

  3. Applied times-frac19.4

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

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

  8. Applied associate-*r*0.8

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

  10. Applied div-inv0.8

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

  11. Applied cbrt-prod0.7

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

  12. Applied associate-*r*0.7

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

  13. Final simplification0.7

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

Reproduce

herbie shell --seed 2020024 
(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))))