Average Error: 33.1 → 0.8
Time: 22.2s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\frac{1}{t}}\right)\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \left(\sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t} \cdot \frac{z}{t}}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\frac{1}{t}}\right)\right)
double f(double x, double y, double z, double t) {
        double r27545223 = x;
        double r27545224 = r27545223 * r27545223;
        double r27545225 = y;
        double r27545226 = r27545225 * r27545225;
        double r27545227 = r27545224 / r27545226;
        double r27545228 = z;
        double r27545229 = r27545228 * r27545228;
        double r27545230 = t;
        double r27545231 = r27545230 * r27545230;
        double r27545232 = r27545229 / r27545231;
        double r27545233 = r27545227 + r27545232;
        return r27545233;
}
↓
double f(double x, double y, double z, double t) {
        double r27545234 = x;
        double r27545235 = y;
        double r27545236 = r27545234 / r27545235;
        double r27545237 = r27545236 * r27545236;
        double r27545238 = z;
        double r27545239 = t;
        double r27545240 = r27545238 / r27545239;
        double r27545241 = r27545240 * r27545240;
        double r27545242 = cbrt(r27545241);
        double r27545243 = r27545242 * r27545242;
        double r27545244 = cbrt(r27545240);
        double r27545245 = cbrt(r27545238);
        double r27545246 = 1.0;
        double r27545247 = r27545246 / r27545239;
        double r27545248 = cbrt(r27545247);
        double r27545249 = r27545245 * r27545248;
        double r27545250 = r27545244 * r27545249;
        double r27545251 = r27545243 * r27545250;
        double r27545252 = r27545237 + r27545251;
        return r27545252;
}

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

Original33.1
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.1

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

  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

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

  6. Applied cbrt-prod0.8

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

  8. Applied div-inv0.8

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

  9. Applied cbrt-prod0.8

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

  10. Final simplification0.8

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

Reproduce

herbie shell --seed 2019192 
(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))))