Average Error: 34.2 → 0.5
Time: 14.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \sqrt{\left|\frac{z}{t}\right|} \cdot {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}}
double f(double x, double y, double z, double t) {
        double r424825 = x;
        double r424826 = r424825 * r424825;
        double r424827 = y;
        double r424828 = r424827 * r424827;
        double r424829 = r424826 / r424828;
        double r424830 = z;
        double r424831 = r424830 * r424830;
        double r424832 = t;
        double r424833 = r424832 * r424832;
        double r424834 = r424831 / r424833;
        double r424835 = r424829 + r424834;
        return r424835;
}
↓
double f(double x, double y, double z, double t) {
        double r424836 = x;
        double r424837 = y;
        double r424838 = r424836 / r424837;
        double r424839 = r424838 * r424838;
        double r424840 = z;
        double r424841 = t;
        double r424842 = r424840 / r424841;
        double r424843 = fabs(r424842);
        double r424844 = sqrt(r424843);
        double r424845 = 1.5;
        double r424846 = pow(r424843, r424845);
        double r424847 = r424844 * r424846;
        double r424848 = r424839 + r424847;
        return r424848;
}

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

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

Derivation

  1. Initial program 34.2

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

  3. Applied add-sqr-sqrt34.2

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

  4. Simplified34.2

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

  5. Simplified19.4

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

  7. Applied times-frac0.4

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

  9. Applied add-sqr-sqrt0.5

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.6

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

  13. Applied pow1/20.6

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

  14. Applied pow-pow0.5

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

  15. Simplified0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 
(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))))