Average Error: 34.0 → 0.5
Time: 4.2s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + {\left(\left|\frac{z}{t}\right|\right)}^{\frac{3}{2}} \cdot \sqrt{\left|\frac{z}{t}\right|}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + {\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 r662158 = x;
        double r662159 = r662158 * r662158;
        double r662160 = y;
        double r662161 = r662160 * r662160;
        double r662162 = r662159 / r662161;
        double r662163 = z;
        double r662164 = r662163 * r662163;
        double r662165 = t;
        double r662166 = r662165 * r662165;
        double r662167 = r662164 / r662166;
        double r662168 = r662162 + r662167;
        return r662168;
}
↓
double f(double x, double y, double z, double t) {
        double r662169 = x;
        double r662170 = y;
        double r662171 = r662169 / r662170;
        double r662172 = r662171 * r662171;
        double r662173 = z;
        double r662174 = t;
        double r662175 = r662173 / r662174;
        double r662176 = fabs(r662175);
        double r662177 = 1.5;
        double r662178 = pow(r662176, r662177);
        double r662179 = sqrt(r662176);
        double r662180 = r662178 * r662179;
        double r662181 = r662172 + r662180;
        return r662181;
}

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

Original34.0
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 34.0

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

  3. Applied times-frac19.3

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

  5. Applied add-sqr-sqrt19.4

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

  6. Simplified19.3

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

  7. Simplified0.4

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

  13. Applied pow1/20.6

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

  14. Applied pow-pow0.5

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

  15. Simplified0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2020081 
(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))))