Average Error: 33.4 → 0.5
Time: 16.8s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
{\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} \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 r449433 = x;
        double r449434 = r449433 * r449433;
        double r449435 = y;
        double r449436 = r449435 * r449435;
        double r449437 = r449434 / r449436;
        double r449438 = z;
        double r449439 = r449438 * r449438;
        double r449440 = t;
        double r449441 = r449440 * r449440;
        double r449442 = r449439 / r449441;
        double r449443 = r449437 + r449442;
        return r449443;
}
↓
double f(double x, double y, double z, double t) {
        double r449444 = x;
        double r449445 = y;
        double r449446 = r449444 / r449445;
        double r449447 = fabs(r449446);
        double r449448 = 1.5;
        double r449449 = pow(r449447, r449448);
        double r449450 = sqrt(r449447);
        double r449451 = r449449 * r449450;
        double r449452 = z;
        double r449453 = t;
        double r449454 = r449452 / r449453;
        double r449455 = r449454 * r449454;
        double r449456 = r449451 + r449455;
        return r449456;
}

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

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

Derivation

  1. Initial program 33.4

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

  3. Applied add-sqr-sqrt33.4

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

  4. Simplified33.4

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

  5. Simplified19.0

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

  7. Applied times-frac0.4

    \[\leadsto \left|\frac{x}{y}\right| \cdot \left|\frac{x}{y}\right| + \color{blue}{\frac{z}{t} \cdot \frac{z}{t}}\]
  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 pow1/20.6

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

  14. Applied pow-pow0.5

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

  15. Simplified0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019208 
(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))))