Average Error: 33.9 → 0.5
Time: 9.7s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left(\left|\frac{x}{y}\right| \cdot \sqrt{\left|\frac{x}{y}\right|}\right) \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left(\left|\frac{x}{y}\right| \cdot \sqrt{\left|\frac{x}{y}\right|}\right) \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r685554 = x;
        double r685555 = r685554 * r685554;
        double r685556 = y;
        double r685557 = r685556 * r685556;
        double r685558 = r685555 / r685557;
        double r685559 = z;
        double r685560 = r685559 * r685559;
        double r685561 = t;
        double r685562 = r685561 * r685561;
        double r685563 = r685560 / r685562;
        double r685564 = r685558 + r685563;
        return r685564;
}
↓
double f(double x, double y, double z, double t) {
        double r685565 = x;
        double r685566 = y;
        double r685567 = r685565 / r685566;
        double r685568 = fabs(r685567);
        double r685569 = sqrt(r685568);
        double r685570 = r685568 * r685569;
        double r685571 = r685570 * r685569;
        double r685572 = z;
        double r685573 = t;
        double r685574 = r685572 / r685573;
        double r685575 = r685574 * r685574;
        double r685576 = r685571 + r685575;
        return r685576;
}

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

Original33.9
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.9

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

  3. Applied times-frac19.1

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

  5. Applied add-sqr-sqrt19.2

    \[\leadsto \color{blue}{\sqrt{\frac{x \cdot x}{y \cdot y}} \cdot \sqrt{\frac{x \cdot x}{y \cdot y}}} + \frac{z}{t} \cdot \frac{z}{t}\]

  6. Simplified19.2

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

  7. Simplified0.4

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

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.6

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

  13. Applied add-cube-cbrt1.2

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

  14. Applied unpow-prod-down1.2

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

  15. Simplified0.8

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

  16. Simplified0.5

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

  17. Final simplification0.5

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

Reproduce

herbie shell --seed 2019350 
(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))))