Average Error: 33.4 → 0.7
Time: 20.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \left(\sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}} \cdot \sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \frac{x}{y}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \left(\sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}} \cdot \sqrt{\sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \frac{x}{y}\right)
double f(double x, double y, double z, double t) {
        double r29400690 = x;
        double r29400691 = r29400690 * r29400690;
        double r29400692 = y;
        double r29400693 = r29400692 * r29400692;
        double r29400694 = r29400691 / r29400693;
        double r29400695 = z;
        double r29400696 = r29400695 * r29400695;
        double r29400697 = t;
        double r29400698 = r29400697 * r29400697;
        double r29400699 = r29400696 / r29400698;
        double r29400700 = r29400694 + r29400699;
        return r29400700;
}
↓
double f(double x, double y, double z, double t) {
        double r29400701 = z;
        double r29400702 = t;
        double r29400703 = r29400701 / r29400702;
        double r29400704 = r29400703 * r29400703;
        double r29400705 = x;
        double r29400706 = y;
        double r29400707 = r29400705 / r29400706;
        double r29400708 = r29400707 * r29400707;
        double r29400709 = cbrt(r29400708);
        double r29400710 = sqrt(r29400709);
        double r29400711 = r29400710 * r29400710;
        double r29400712 = cbrt(r29400707);
        double r29400713 = r29400712 * r29400707;
        double r29400714 = r29400711 * r29400713;
        double r29400715 = r29400704 + r29400714;
        return r29400715;
}

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

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

Derivation

  1. Initial program 33.4

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

  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

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

  5. Applied associate-*l*0.8

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

  7. Applied cbrt-unprod0.6

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

  9. Applied add-sqr-sqrt0.7

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

  10. Final simplification0.7

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

Reproduce

herbie shell --seed 2019172 
(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))))