Average Error: 33.7 → 0.9
Time: 20.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{z}}{\sqrt[3]{t}} \cdot \frac{z}{t}\right) + \frac{x}{y} \cdot \frac{x}{y}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\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}{y} \cdot \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r27825674 = x;
        double r27825675 = r27825674 * r27825674;
        double r27825676 = y;
        double r27825677 = r27825676 * r27825676;
        double r27825678 = r27825675 / r27825677;
        double r27825679 = z;
        double r27825680 = r27825679 * r27825679;
        double r27825681 = t;
        double r27825682 = r27825681 * r27825681;
        double r27825683 = r27825680 / r27825682;
        double r27825684 = r27825678 + r27825683;
        return r27825684;
}
↓
double f(double x, double y, double z, double t) {
        double r27825685 = z;
        double r27825686 = cbrt(r27825685);
        double r27825687 = r27825686 * r27825686;
        double r27825688 = t;
        double r27825689 = cbrt(r27825688);
        double r27825690 = r27825689 * r27825689;
        double r27825691 = r27825687 / r27825690;
        double r27825692 = r27825686 / r27825689;
        double r27825693 = r27825685 / r27825688;
        double r27825694 = r27825692 * r27825693;
        double r27825695 = r27825691 * r27825694;
        double r27825696 = x;
        double r27825697 = y;
        double r27825698 = r27825696 / r27825697;
        double r27825699 = r27825698 * r27825698;
        double r27825700 = r27825695 + r27825699;
        return r27825700;
}

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

Derivation

  1. Initial program 33.7

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

  2. 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

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

  5. Applied add-cube-cbrt0.9

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

  6. Applied times-frac0.9

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

  7. Applied associate-*l*0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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