Average Error: 32.3 → 0.7
Time: 17.5s
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 r26786173 = x;
        double r26786174 = r26786173 * r26786173;
        double r26786175 = y;
        double r26786176 = r26786175 * r26786175;
        double r26786177 = r26786174 / r26786176;
        double r26786178 = z;
        double r26786179 = r26786178 * r26786178;
        double r26786180 = t;
        double r26786181 = r26786180 * r26786180;
        double r26786182 = r26786179 / r26786181;
        double r26786183 = r26786177 + r26786182;
        return r26786183;
}
↓
double f(double x, double y, double z, double t) {
        double r26786184 = x;
        double r26786185 = y;
        double r26786186 = r26786184 / r26786185;
        double r26786187 = cbrt(r26786186);
        double r26786188 = 1.0;
        double r26786189 = r26786188 / r26786185;
        double r26786190 = cbrt(r26786189);
        double r26786191 = r26786187 * r26786190;
        double r26786192 = cbrt(r26786184);
        double r26786193 = r26786191 * r26786192;
        double r26786194 = r26786186 * r26786193;
        double r26786195 = r26786187 * r26786194;
        double r26786196 = z;
        double r26786197 = t;
        double r26786198 = r26786196 / r26786197;
        double r26786199 = r26786198 * r26786198;
        double r26786200 = r26786195 + r26786199;
        return r26786200;
}

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

Original32.3
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))))