Average Error: 33.0 → 0.8
Time: 24.7s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \frac{x}{y}\right) \cdot \left(\sqrt[3]{\frac{x}{\sqrt[3]{y}}} \cdot \sqrt[3]{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \frac{x}{y}\right) \cdot \left(\sqrt[3]{\frac{x}{\sqrt[3]{y}}} \cdot \sqrt[3]{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}\right)
double f(double x, double y, double z, double t) {
        double r26057657 = x;
        double r26057658 = r26057657 * r26057657;
        double r26057659 = y;
        double r26057660 = r26057659 * r26057659;
        double r26057661 = r26057658 / r26057660;
        double r26057662 = z;
        double r26057663 = r26057662 * r26057662;
        double r26057664 = t;
        double r26057665 = r26057664 * r26057664;
        double r26057666 = r26057663 / r26057665;
        double r26057667 = r26057661 + r26057666;
        return r26057667;
}
↓
double f(double x, double y, double z, double t) {
        double r26057668 = z;
        double r26057669 = t;
        double r26057670 = r26057668 / r26057669;
        double r26057671 = r26057670 * r26057670;
        double r26057672 = x;
        double r26057673 = y;
        double r26057674 = r26057672 / r26057673;
        double r26057675 = cbrt(r26057674);
        double r26057676 = r26057675 * r26057675;
        double r26057677 = r26057676 * r26057674;
        double r26057678 = cbrt(r26057673);
        double r26057679 = r26057672 / r26057678;
        double r26057680 = cbrt(r26057679);
        double r26057681 = 1.0;
        double r26057682 = r26057678 * r26057678;
        double r26057683 = r26057681 / r26057682;
        double r26057684 = cbrt(r26057683);
        double r26057685 = r26057680 * r26057684;
        double r26057686 = r26057677 * r26057685;
        double r26057687 = r26057671 + r26057686;
        return r26057687;
}

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

Original33.0
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.0

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

  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 add-cube-cbrt0.8

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

  8. Applied *-un-lft-identity0.8

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

  9. Applied times-frac0.8

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

  10. Applied cbrt-prod0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2019165 
(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))))