Average Error: 34.3 → 0.5
Time: 12.4s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + {\left(\left|\frac{z}{t}\right|\right)}^{\left(\frac{1}{2} \cdot 3\right)} \cdot \sqrt{\left|\frac{z}{t}\right|}\]
\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)}^{\left(\frac{1}{2} \cdot 3\right)} \cdot \sqrt{\left|\frac{z}{t}\right|}
double f(double x, double y, double z, double t) {
        double r428167 = x;
        double r428168 = r428167 * r428167;
        double r428169 = y;
        double r428170 = r428169 * r428169;
        double r428171 = r428168 / r428170;
        double r428172 = z;
        double r428173 = r428172 * r428172;
        double r428174 = t;
        double r428175 = r428174 * r428174;
        double r428176 = r428173 / r428175;
        double r428177 = r428171 + r428176;
        return r428177;
}
↓
double f(double x, double y, double z, double t) {
        double r428178 = x;
        double r428179 = y;
        double r428180 = r428178 / r428179;
        double r428181 = r428180 * r428180;
        double r428182 = z;
        double r428183 = t;
        double r428184 = r428182 / r428183;
        double r428185 = fabs(r428184);
        double r428186 = 0.5;
        double r428187 = 3.0;
        double r428188 = r428186 * r428187;
        double r428189 = pow(r428185, r428188);
        double r428190 = sqrt(r428185);
        double r428191 = r428189 * r428190;
        double r428192 = r428181 + r428191;
        return r428192;
}

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

Original34.3
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 34.3

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

  3. Applied add-sqr-sqrt34.4

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

  4. Simplified34.3

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

  5. Simplified19.1

    \[\leadsto \frac{x \cdot x}{y \cdot y} + \left|\frac{z}{t}\right| \cdot \color{blue}{\left|\frac{z}{t}\right|}\]
  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. 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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019291 
(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))))