Average Error: 33.2 → 0.4
Time: 14.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r425269 = x;
        double r425270 = r425269 * r425269;
        double r425271 = y;
        double r425272 = r425271 * r425271;
        double r425273 = r425270 / r425272;
        double r425274 = z;
        double r425275 = r425274 * r425274;
        double r425276 = t;
        double r425277 = r425276 * r425276;
        double r425278 = r425275 / r425277;
        double r425279 = r425273 + r425278;
        return r425279;
}
↓
double f(double x, double y, double z, double t) {
        double r425280 = x;
        double r425281 = y;
        double r425282 = r425280 / r425281;
        double r425283 = fabs(r425282);
        double r425284 = sqrt(r425283);
        double r425285 = 1.5;
        double r425286 = pow(r425283, r425285);
        double r425287 = r425284 * r425286;
        double r425288 = z;
        double r425289 = t;
        double r425290 = r425288 / r425289;
        double r425291 = r425290 * r425290;
        double r425292 = r425287 + r425291;
        return r425292;
}

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

Original33.2
Target0.4
Herbie0.4
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.2

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

  3. Applied times-frac19.0

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

  5. Applied add-sqr-sqrt19.0

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

  6. Simplified19.0

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

  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

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.6

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

  13. Applied pow1/20.6

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

  14. Applied pow-pow0.4

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

  15. Simplified0.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 
(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))))