Average Error: 32.3 → 0.7
Time: 19.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt[3]{\frac{x}{y}} \cdot \left(\frac{x}{y} \cdot \left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{1}{y}}\right) \cdot \sqrt[3]{x}\right)\right) + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt[3]{\frac{x}{y}} \cdot \left(\frac{x}{y} \cdot \left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{1}{y}}\right) \cdot \sqrt[3]{x}\right)\right) + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r30355221 = x;
        double r30355222 = r30355221 * r30355221;
        double r30355223 = y;
        double r30355224 = r30355223 * r30355223;
        double r30355225 = r30355222 / r30355224;
        double r30355226 = z;
        double r30355227 = r30355226 * r30355226;
        double r30355228 = t;
        double r30355229 = r30355228 * r30355228;
        double r30355230 = r30355227 / r30355229;
        double r30355231 = r30355225 + r30355230;
        return r30355231;
}
↓
double f(double x, double y, double z, double t) {
        double r30355232 = x;
        double r30355233 = y;
        double r30355234 = r30355232 / r30355233;
        double r30355235 = cbrt(r30355234);
        double r30355236 = 1.0;
        double r30355237 = r30355236 / r30355233;
        double r30355238 = cbrt(r30355237);
        double r30355239 = r30355235 * r30355238;
        double r30355240 = cbrt(r30355232);
        double r30355241 = r30355239 * r30355240;
        double r30355242 = r30355234 * r30355241;
        double r30355243 = r30355235 * r30355242;
        double r30355244 = z;
        double r30355245 = t;
        double r30355246 = r30355244 / r30355245;
        double r30355247 = r30355246 * r30355246;
        double r30355248 = r30355243 + r30355247;
        return r30355248;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.3
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 32.3

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

  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

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

  5. Applied associate-*r*0.8

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

  7. Applied div-inv0.8

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

  8. Applied cbrt-prod0.7

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

  9. Applied associate-*l*0.7

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

  10. Final simplification0.7

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

Reproduce

herbie shell --seed 2019162 
(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))))