Average Error: 33.6 → 0.9
Time: 6.2s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\frac{x}{y} \cdot \frac{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\frac{x}{y} \cdot \frac{\sqrt[3]{x} \cdot \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right)}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r648468 = x;
        double r648469 = r648468 * r648468;
        double r648470 = y;
        double r648471 = r648470 * r648470;
        double r648472 = r648469 / r648471;
        double r648473 = z;
        double r648474 = r648473 * r648473;
        double r648475 = t;
        double r648476 = r648475 * r648475;
        double r648477 = r648474 / r648476;
        double r648478 = r648472 + r648477;
        return r648478;
}
↓
double f(double x, double y, double z, double t) {
        double r648479 = x;
        double r648480 = y;
        double r648481 = r648479 / r648480;
        double r648482 = cbrt(r648479);
        double r648483 = r648482 * r648482;
        double r648484 = cbrt(r648483);
        double r648485 = cbrt(r648482);
        double r648486 = r648484 * r648485;
        double r648487 = r648482 * r648486;
        double r648488 = cbrt(r648480);
        double r648489 = r648488 * r648488;
        double r648490 = r648487 / r648489;
        double r648491 = r648481 * r648490;
        double r648492 = r648482 / r648488;
        double r648493 = r648491 * r648492;
        double r648494 = z;
        double r648495 = t;
        double r648496 = r648494 / r648495;
        double r648497 = r648496 * r648496;
        double r648498 = r648493 + r648497;
        return r648498;
}

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

Original33.6
Target0.4
Herbie0.9
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.6

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

  3. Applied times-frac18.7

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

  5. Applied times-frac0.4

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

  7. Applied add-cube-cbrt0.8

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

  8. Applied add-cube-cbrt0.9

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

  9. Applied times-frac0.9

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

  10. Applied associate-*r*0.9

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

  12. Applied add-cube-cbrt0.9

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

  13. Applied cbrt-prod0.9

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

  14. Final simplification0.9

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

Reproduce

herbie shell --seed 2019322 
(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))))