Average Error: 33.8 → 0.9
Time: 7.7s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{z}{t}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{z}{t}\right)
double f(double x, double y, double z, double t) {
        double r764793 = x;
        double r764794 = r764793 * r764793;
        double r764795 = y;
        double r764796 = r764795 * r764795;
        double r764797 = r764794 / r764796;
        double r764798 = z;
        double r764799 = r764798 * r764798;
        double r764800 = t;
        double r764801 = r764800 * r764800;
        double r764802 = r764799 / r764801;
        double r764803 = r764797 + r764802;
        return r764803;
}
↓
double f(double x, double y, double z, double t) {
        double r764804 = x;
        double r764805 = y;
        double r764806 = r764804 / r764805;
        double r764807 = r764806 * r764806;
        double r764808 = z;
        double r764809 = cbrt(r764808);
        double r764810 = r764809 * r764809;
        double r764811 = t;
        double r764812 = cbrt(r764811);
        double r764813 = r764812 * r764812;
        double r764814 = r764810 / r764813;
        double r764815 = r764809 / r764812;
        double r764816 = r764808 / r764811;
        double r764817 = r764815 * r764816;
        double r764818 = r764814 * r764817;
        double r764819 = r764807 + r764818;
        return r764819;
}

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
Herbie0.9
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

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-frac19.4

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

  5. Applied times-frac0.4

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

  7. Applied add-cube-cbrt0.8

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

  8. Applied add-cube-cbrt0.9

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

  9. Applied times-frac0.9

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

  10. Applied associate-*l*0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2020045 
(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))))