Average Error: 33.3 → 0.8
Time: 4.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\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}
double f(double x, double y, double z, double t) {
        double r808193 = x;
        double r808194 = r808193 * r808193;
        double r808195 = y;
        double r808196 = r808195 * r808195;
        double r808197 = r808194 / r808196;
        double r808198 = z;
        double r808199 = r808198 * r808198;
        double r808200 = t;
        double r808201 = r808200 * r808200;
        double r808202 = r808199 / r808201;
        double r808203 = r808197 + r808202;
        return r808203;
}
↓
double f(double x, double y, double z, double t) {
        double r808204 = x;
        double r808205 = y;
        double r808206 = r808204 / r808205;
        double r808207 = r808206 * r808206;
        double r808208 = cbrt(r808207);
        double r808209 = r808208 * r808208;
        double r808210 = r808209 * r808208;
        double r808211 = z;
        double r808212 = t;
        double r808213 = r808211 / r808212;
        double r808214 = r808213 * r808213;
        double r808215 = r808210 + r808214;
        return r808215;
}

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

Original33.3
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.3

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
  2. Using strategy rm

  3. Applied times-frac18.8

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

  5. Applied times-frac0.4

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

  7. Applied add-cube-cbrt0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2) (pow (/ z t) 2))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))