Average Error: 33.9 → 0.7
Time: 20.6s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \left(\frac{\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{x}}{\sqrt[3]{y}} \cdot \frac{x}{y}\right) \cdot \sqrt[3]{\frac{x}{y}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \left(\frac{\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{x}}{\sqrt[3]{y}} \cdot \frac{x}{y}\right) \cdot \sqrt[3]{\frac{x}{y}}
double f(double x, double y, double z, double t) {
        double r32851787 = x;
        double r32851788 = r32851787 * r32851787;
        double r32851789 = y;
        double r32851790 = r32851789 * r32851789;
        double r32851791 = r32851788 / r32851790;
        double r32851792 = z;
        double r32851793 = r32851792 * r32851792;
        double r32851794 = t;
        double r32851795 = r32851794 * r32851794;
        double r32851796 = r32851793 / r32851795;
        double r32851797 = r32851791 + r32851796;
        return r32851797;
}
↓
double f(double x, double y, double z, double t) {
        double r32851798 = z;
        double r32851799 = t;
        double r32851800 = r32851798 / r32851799;
        double r32851801 = r32851800 * r32851800;
        double r32851802 = x;
        double r32851803 = y;
        double r32851804 = r32851802 / r32851803;
        double r32851805 = cbrt(r32851804);
        double r32851806 = cbrt(r32851802);
        double r32851807 = r32851805 * r32851806;
        double r32851808 = cbrt(r32851803);
        double r32851809 = r32851807 / r32851808;
        double r32851810 = r32851809 * r32851804;
        double r32851811 = r32851810 * r32851805;
        double r32851812 = r32851801 + r32851811;
        return r32851812;
}

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

Original33.9
Target0.4
Herbie0.7
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.9

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

  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 cbrt-div0.7

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

  8. Applied associate-*r/0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2019171 
(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))))