Average Error: 32.2 → 0.8
Time: 16.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \left(\frac{x}{y} \cdot \left(\left(\sqrt[3]{\frac{1}{y}} \cdot \sqrt[3]{x}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot \sqrt[3]{\frac{x}{y}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \left(\frac{x}{y} \cdot \left(\left(\sqrt[3]{\frac{1}{y}} \cdot \sqrt[3]{x}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot \sqrt[3]{\frac{x}{y}}
double f(double x, double y, double z, double t) {
        double r30586850 = x;
        double r30586851 = r30586850 * r30586850;
        double r30586852 = y;
        double r30586853 = r30586852 * r30586852;
        double r30586854 = r30586851 / r30586853;
        double r30586855 = z;
        double r30586856 = r30586855 * r30586855;
        double r30586857 = t;
        double r30586858 = r30586857 * r30586857;
        double r30586859 = r30586856 / r30586858;
        double r30586860 = r30586854 + r30586859;
        return r30586860;
}
↓
double f(double x, double y, double z, double t) {
        double r30586861 = z;
        double r30586862 = t;
        double r30586863 = r30586861 / r30586862;
        double r30586864 = r30586863 * r30586863;
        double r30586865 = x;
        double r30586866 = y;
        double r30586867 = r30586865 / r30586866;
        double r30586868 = 1.0;
        double r30586869 = r30586868 / r30586866;
        double r30586870 = cbrt(r30586869);
        double r30586871 = cbrt(r30586865);
        double r30586872 = r30586870 * r30586871;
        double r30586873 = cbrt(r30586866);
        double r30586874 = r30586871 / r30586873;
        double r30586875 = r30586872 * r30586874;
        double r30586876 = r30586867 * r30586875;
        double r30586877 = cbrt(r30586867);
        double r30586878 = r30586876 * r30586877;
        double r30586879 = r30586864 + r30586878;
        return r30586879;
}

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

Original32.2
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 32.2

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

  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-cube-cbrt0.8

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

  5. Applied associate-*r*0.8

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

  6. Taylor expanded around 0 46.2

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

  7. Simplified0.7

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

  9. Applied cbrt-div0.8

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

  10. Final simplification0.8

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))