Average Error: 33.8 → 0.9
Time: 14.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{z}{t} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right) + \frac{x}{y} \cdot \frac{x}{y}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{z}{t} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\right) + \frac{x}{y} \cdot \frac{x}{y}
double f(double x, double y, double z, double t) {
        double r423193 = x;
        double r423194 = r423193 * r423193;
        double r423195 = y;
        double r423196 = r423195 * r423195;
        double r423197 = r423194 / r423196;
        double r423198 = z;
        double r423199 = r423198 * r423198;
        double r423200 = t;
        double r423201 = r423200 * r423200;
        double r423202 = r423199 / r423201;
        double r423203 = r423197 + r423202;
        return r423203;
}
↓
double f(double x, double y, double z, double t) {
        double r423204 = z;
        double r423205 = cbrt(r423204);
        double r423206 = r423205 * r423205;
        double r423207 = t;
        double r423208 = cbrt(r423207);
        double r423209 = r423208 * r423208;
        double r423210 = r423206 / r423209;
        double r423211 = r423204 / r423207;
        double r423212 = r423205 / r423208;
        double r423213 = r423211 * r423212;
        double r423214 = r423210 * r423213;
        double r423215 = x;
        double r423216 = y;
        double r423217 = r423215 / r423216;
        double r423218 = r423217 * r423217;
        double r423219 = r423214 + r423218;
        return r423219;
}

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

Original33.8
Target0.4
Herbie0.9
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.8

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

  2. Simplified13.2

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

  3. Taylor expanded around 0 19.2

    \[\leadsto \color{blue}{\frac{{x}^{2}}{{y}^{2}}} + \frac{z}{t} \cdot \frac{z}{t}\]

  4. Simplified0.4

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z}{t} \cdot \frac{z}{t}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.8

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

  7. Applied add-cube-cbrt0.9

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

  8. Applied times-frac0.9

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

  9. Applied associate-*l*0.9

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

  10. Simplified0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019195 
(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))))