Average Error: 34.1 → 0.5
Time: 9.9s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[{\left(\left|\frac{x}{y}\right|\right)}^{\left(\frac{3}{2}\right)} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
{\left(\left|\frac{x}{y}\right|\right)}^{\left(\frac{3}{2}\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 r462543 = x;
        double r462544 = r462543 * r462543;
        double r462545 = y;
        double r462546 = r462545 * r462545;
        double r462547 = r462544 / r462546;
        double r462548 = z;
        double r462549 = r462548 * r462548;
        double r462550 = t;
        double r462551 = r462550 * r462550;
        double r462552 = r462549 / r462551;
        double r462553 = r462547 + r462552;
        return r462553;
}
↓
double f(double x, double y, double z, double t) {
        double r462554 = x;
        double r462555 = y;
        double r462556 = r462554 / r462555;
        double r462557 = fabs(r462556);
        double r462558 = 3.0;
        double r462559 = 2.0;
        double r462560 = r462558 / r462559;
        double r462561 = pow(r462557, r462560);
        double r462562 = sqrt(r462557);
        double r462563 = r462561 * r462562;
        double r462564 = z;
        double r462565 = t;
        double r462566 = r462564 / r462565;
        double r462567 = r462566 * r462566;
        double r462568 = r462563 + r462567;
        return r462568;
}

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

Original34.1
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 34.1

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

  3. Applied times-frac19.4

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

  5. Applied add-sqr-sqrt19.4

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

  6. Simplified19.4

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

  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 pow10.6

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

  14. Applied sqrt-pow10.6

    \[\leadsto {\color{blue}{\left({\left(\left|\frac{x}{y}\right|\right)}^{\left(\frac{1}{2}\right)}\right)}}^{3} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

  15. Applied pow-pow0.5

    \[\leadsto \color{blue}{{\left(\left|\frac{x}{y}\right|\right)}^{\left(\frac{1}{2} \cdot 3\right)}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

  16. Simplified0.5

    \[\leadsto {\left(\left|\frac{x}{y}\right|\right)}^{\color{blue}{\left(\frac{3}{2}\right)}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

  17. Final simplification0.5

    \[\leadsto {\left(\left|\frac{x}{y}\right|\right)}^{\left(\frac{3}{2}\right)} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]

Reproduce

herbie shell --seed 2019297 
(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))))