Average Error: 33.7 → 0.6
Time: 4.0s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3} \cdot \sqrt{\left|\frac{z}{t}\right|}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + {\left(\sqrt{\left|\frac{z}{t}\right|}\right)}^{3} \cdot \sqrt{\left|\frac{z}{t}\right|}
double f(double x, double y, double z, double t) {
        double r619822 = x;
        double r619823 = r619822 * r619822;
        double r619824 = y;
        double r619825 = r619824 * r619824;
        double r619826 = r619823 / r619825;
        double r619827 = z;
        double r619828 = r619827 * r619827;
        double r619829 = t;
        double r619830 = r619829 * r619829;
        double r619831 = r619828 / r619830;
        double r619832 = r619826 + r619831;
        return r619832;
}
↓
double f(double x, double y, double z, double t) {
        double r619833 = x;
        double r619834 = y;
        double r619835 = r619833 / r619834;
        double r619836 = r619835 * r619835;
        double r619837 = z;
        double r619838 = t;
        double r619839 = r619837 / r619838;
        double r619840 = fabs(r619839);
        double r619841 = sqrt(r619840);
        double r619842 = 3.0;
        double r619843 = pow(r619841, r619842);
        double r619844 = r619843 * r619841;
        double r619845 = r619836 + r619844;
        return r619845;
}

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
Herbie0.6
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

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

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

  4. Simplified33.7

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

  5. Simplified19.3

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

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2020049 
(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))))