Average Error: 33.3 → 0.8
Time: 3.8s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r581084 = x;
        double r581085 = r581084 * r581084;
        double r581086 = y;
        double r581087 = r581086 * r581086;
        double r581088 = r581085 / r581087;
        double r581089 = z;
        double r581090 = r581089 * r581089;
        double r581091 = t;
        double r581092 = r581091 * r581091;
        double r581093 = r581090 / r581092;
        double r581094 = r581088 + r581093;
        return r581094;
}
↓
double f(double x, double y, double z, double t) {
        double r581095 = x;
        double r581096 = y;
        double r581097 = r581095 / r581096;
        double r581098 = r581097 * r581097;
        double r581099 = cbrt(r581098);
        double r581100 = r581099 * r581099;
        double r581101 = r581100 * r581099;
        double r581102 = z;
        double r581103 = t;
        double r581104 = r581102 / r581103;
        double r581105 = r581104 * r581104;
        double r581106 = r581101 + r581105;
        return r581106;
}

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

Original33.3
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.3

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

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2020021 
(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))))