Average Error: 34.3 → 0.8
Time: 46.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \left(\left(\sqrt[3]{\frac{x}{y}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \sqrt[3]{\frac{x}{\sqrt[3]{y}}}\right)\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \left(\left(\sqrt[3]{\frac{x}{y}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \sqrt[3]{\frac{x}{\sqrt[3]{y}}}\right)\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y} \cdot \frac{x}{y}}
double f(double x, double y, double z, double t) {
        double r32537595 = x;
        double r32537596 = r32537595 * r32537595;
        double r32537597 = y;
        double r32537598 = r32537597 * r32537597;
        double r32537599 = r32537596 / r32537598;
        double r32537600 = z;
        double r32537601 = r32537600 * r32537600;
        double r32537602 = t;
        double r32537603 = r32537602 * r32537602;
        double r32537604 = r32537601 / r32537603;
        double r32537605 = r32537599 + r32537604;
        return r32537605;
}
↓
double f(double x, double y, double z, double t) {
        double r32537606 = z;
        double r32537607 = t;
        double r32537608 = r32537606 / r32537607;
        double r32537609 = r32537608 * r32537608;
        double r32537610 = x;
        double r32537611 = y;
        double r32537612 = r32537610 / r32537611;
        double r32537613 = cbrt(r32537612);
        double r32537614 = 1.0;
        double r32537615 = cbrt(r32537611);
        double r32537616 = r32537615 * r32537615;
        double r32537617 = r32537614 / r32537616;
        double r32537618 = cbrt(r32537617);
        double r32537619 = r32537610 / r32537615;
        double r32537620 = cbrt(r32537619);
        double r32537621 = r32537618 * r32537620;
        double r32537622 = r32537613 * r32537621;
        double r32537623 = r32537612 * r32537612;
        double r32537624 = cbrt(r32537623);
        double r32537625 = r32537622 * r32537624;
        double r32537626 = r32537625 * r32537624;
        double r32537627 = r32537609 + r32537626;
        return r32537627;
}

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

Original34.3
Target0.4
Herbie0.8
\[{\left(\frac{x}{y}\right)}^{2.0} + {\left(\frac{z}{t}\right)}^{2.0}\]

Derivation

  1. Initial program 34.3

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

  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

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

  6. Applied cbrt-prod0.8

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

  8. Applied add-cube-cbrt0.8

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

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

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

  10. Applied times-frac0.8

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

  11. Applied cbrt-prod0.8

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

  12. Final simplification0.8

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

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) 2.0) (pow (/ z t) 2.0))

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