Average Error: 33.7 → 0.5
Time: 18.7s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{z}{t}\right|}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{z}{t}\right|}
double f(double x, double y, double z, double t) {
        double r514342 = x;
        double r514343 = r514342 * r514342;
        double r514344 = y;
        double r514345 = r514344 * r514344;
        double r514346 = r514343 / r514345;
        double r514347 = z;
        double r514348 = r514347 * r514347;
        double r514349 = t;
        double r514350 = r514349 * r514349;
        double r514351 = r514348 / r514350;
        double r514352 = r514346 + r514351;
        return r514352;
}
↓
double f(double x, double y, double z, double t) {
        double r514353 = x;
        double r514354 = y;
        double r514355 = r514353 / r514354;
        double r514356 = fabs(r514355);
        double r514357 = r514356 * r514356;
        double r514358 = z;
        double r514359 = t;
        double r514360 = r514358 / r514359;
        double r514361 = fabs(r514360);
        double r514362 = 1.5;
        double r514363 = pow(r514361, r514362);
        double r514364 = sqrt(r514361);
        double r514365 = r514363 * r514364;
        double r514366 = r514357 + r514365;
        return r514366;
}

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

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 add-sqr-sqrt33.7

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

  4. Simplified33.7

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

  5. Simplified18.9

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

  7. Applied add-sqr-sqrt18.9

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

  8. Simplified18.9

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

  9. Simplified0.4

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

  11. Applied add-sqr-sqrt0.5

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

  12. Applied associate-*r*0.5

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

  13. Simplified0.6

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

  15. Applied pow1/20.6

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

  16. Applied pow-pow0.5

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

  17. Simplified0.5

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

  18. Final simplification0.5

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

Reproduce

herbie shell --seed 2019199 
(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))))