Average Error: 31.9 → 0.8
Time: 18.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r32129261 = x;
        double r32129262 = r32129261 * r32129261;
        double r32129263 = y;
        double r32129264 = r32129263 * r32129263;
        double r32129265 = r32129262 / r32129264;
        double r32129266 = z;
        double r32129267 = r32129266 * r32129266;
        double r32129268 = t;
        double r32129269 = r32129268 * r32129268;
        double r32129270 = r32129267 / r32129269;
        double r32129271 = r32129265 + r32129270;
        return r32129271;
}
↓
double f(double x, double y, double z, double t) {
        double r32129272 = x;
        double r32129273 = y;
        double r32129274 = r32129272 / r32129273;
        double r32129275 = r32129274 * r32129274;
        double r32129276 = cbrt(r32129275);
        double r32129277 = cbrt(r32129274);
        double r32129278 = cbrt(r32129272);
        double r32129279 = cbrt(r32129273);
        double r32129280 = r32129278 / r32129279;
        double r32129281 = r32129277 * r32129280;
        double r32129282 = r32129276 * r32129281;
        double r32129283 = r32129276 * r32129282;
        double r32129284 = z;
        double r32129285 = t;
        double r32129286 = r32129284 / r32129285;
        double r32129287 = r32129286 * r32129286;
        double r32129288 = r32129283 + r32129287;
        return r32129288;
}

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

Original31.9
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 31.9

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

  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

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

  6. Applied cbrt-prod0.8

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

  8. Applied cbrt-div0.8

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

  9. Final simplification0.8

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

Reproduce

herbie shell --seed 2019158 
(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))))