Average Error: 33.7 → 0.8
Time: 4.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \left(\frac{z}{t} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right)\right)\right) \cdot \sqrt[3]{\frac{z}{t}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \left(\frac{z}{t} \cdot \left(\sqrt[3]{\frac{z}{t}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right)\right)\right) \cdot \sqrt[3]{\frac{z}{t}}
double f(double x, double y, double z, double t) {
        double r820656 = x;
        double r820657 = r820656 * r820656;
        double r820658 = y;
        double r820659 = r820658 * r820658;
        double r820660 = r820657 / r820659;
        double r820661 = z;
        double r820662 = r820661 * r820661;
        double r820663 = t;
        double r820664 = r820663 * r820663;
        double r820665 = r820662 / r820664;
        double r820666 = r820660 + r820665;
        return r820666;
}
↓
double f(double x, double y, double z, double t) {
        double r820667 = x;
        double r820668 = y;
        double r820669 = r820667 / r820668;
        double r820670 = r820669 * r820669;
        double r820671 = z;
        double r820672 = t;
        double r820673 = r820671 / r820672;
        double r820674 = cbrt(r820673);
        double r820675 = 1.0;
        double r820676 = cbrt(r820672);
        double r820677 = r820676 * r820676;
        double r820678 = r820675 / r820677;
        double r820679 = cbrt(r820678);
        double r820680 = r820671 / r820676;
        double r820681 = cbrt(r820680);
        double r820682 = r820679 * r820681;
        double r820683 = r820674 * r820682;
        double r820684 = r820673 * r820683;
        double r820685 = r820684 * r820674;
        double r820686 = r820670 + r820685;
        return r820686;
}

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

Original33.7
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.7

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

  3. Applied times-frac18.9

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

  5. Applied times-frac0.4

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

  7. Applied add-cube-cbrt0.8

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

  8. Applied associate-*r*0.8

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

  10. Applied add-cube-cbrt0.8

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

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

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

  12. Applied times-frac0.8

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

  13. Applied cbrt-prod0.8

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

  14. Final simplification0.8

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

Reproduce

herbie shell --seed 2020046 
(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))))