Average Error: 34.1 → 0.5
Time: 21.5s
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 r508311 = x;
        double r508312 = r508311 * r508311;
        double r508313 = y;
        double r508314 = r508313 * r508313;
        double r508315 = r508312 / r508314;
        double r508316 = z;
        double r508317 = r508316 * r508316;
        double r508318 = t;
        double r508319 = r508318 * r508318;
        double r508320 = r508317 / r508319;
        double r508321 = r508315 + r508320;
        return r508321;
}
↓
double f(double x, double y, double z, double t) {
        double r508322 = x;
        double r508323 = y;
        double r508324 = r508322 / r508323;
        double r508325 = fabs(r508324);
        double r508326 = sqrt(r508325);
        double r508327 = r508325 * r508326;
        double r508328 = r508327 * r508326;
        double r508329 = z;
        double r508330 = t;
        double r508331 = r508329 / r508330;
        double r508332 = r508331 * r508331;
        double r508333 = r508328 + r508332;
        return r508333;
}

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-frac19.6

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

  5. Applied add-sqr-sqrt19.6

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

  6. Simplified19.6

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

  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-cbrt1.3

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

  14. Applied unpow-prod-down1.3

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

  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 2019198 
(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))))