Average Error: 32.2 → 0.7
Time: 16.6s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\left(\sqrt[3]{\frac{1}{t}} \cdot \sqrt[3]{z}\right) \cdot \frac{z}{t}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right) + \frac{x}{y} \cdot \frac{x}{y}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\left(\sqrt[3]{\frac{1}{t}} \cdot \sqrt[3]{z}\right) \cdot \frac{z}{t}\right) \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \sqrt[3]{\frac{z}{t}}\right) + \frac{x}{y} \cdot \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r32075163 = x;
        double r32075164 = r32075163 * r32075163;
        double r32075165 = y;
        double r32075166 = r32075165 * r32075165;
        double r32075167 = r32075164 / r32075166;
        double r32075168 = z;
        double r32075169 = r32075168 * r32075168;
        double r32075170 = t;
        double r32075171 = r32075170 * r32075170;
        double r32075172 = r32075169 / r32075171;
        double r32075173 = r32075167 + r32075172;
        return r32075173;
}
↓
double f(double x, double y, double z, double t) {
        double r32075174 = 1.0;
        double r32075175 = t;
        double r32075176 = r32075174 / r32075175;
        double r32075177 = cbrt(r32075176);
        double r32075178 = z;
        double r32075179 = cbrt(r32075178);
        double r32075180 = r32075177 * r32075179;
        double r32075181 = r32075178 / r32075175;
        double r32075182 = r32075180 * r32075181;
        double r32075183 = cbrt(r32075181);
        double r32075184 = r32075183 * r32075183;
        double r32075185 = r32075182 * r32075184;
        double r32075186 = x;
        double r32075187 = y;
        double r32075188 = r32075186 / r32075187;
        double r32075189 = r32075188 * r32075188;
        double r32075190 = r32075185 + r32075189;
        return r32075190;
}

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

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

Derivation

  1. Initial program 32.2

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

  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

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

  5. Applied associate-*l*0.8

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

  6. Taylor expanded around 0 46.7

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

  7. Simplified0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019163 
(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))))