Average Error: 32.5 → 0.6
Time: 13.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\frac{z}{t} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t}}\]
\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 \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \sqrt[3]{\frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r11330023 = x;
        double r11330024 = r11330023 * r11330023;
        double r11330025 = y;
        double r11330026 = r11330025 * r11330025;
        double r11330027 = r11330024 / r11330026;
        double r11330028 = z;
        double r11330029 = r11330028 * r11330028;
        double r11330030 = t;
        double r11330031 = r11330030 * r11330030;
        double r11330032 = r11330029 / r11330031;
        double r11330033 = r11330027 + r11330032;
        return r11330033;
}
↓
double f(double x, double y, double z, double t) {
        double r11330034 = x;
        double r11330035 = y;
        double r11330036 = r11330034 / r11330035;
        double r11330037 = r11330036 * r11330036;
        double r11330038 = z;
        double r11330039 = t;
        double r11330040 = r11330038 / r11330039;
        double r11330041 = r11330040 * r11330040;
        double r11330042 = cbrt(r11330041);
        double r11330043 = r11330040 * r11330042;
        double r11330044 = cbrt(r11330040);
        double r11330045 = r11330043 * r11330044;
        double r11330046 = r11330037 + r11330045;
        return r11330046;
}

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

Original32.5
Target0.4
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 32.5

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

  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

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

  5. Applied associate-*r*0.8

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

  7. Applied cbrt-unprod0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019156 
(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))))