Average Error: 33.9 → 0.5
Time: 4.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\sqrt{\left|\frac{x}{y}\right|} \cdot {\left(\left|\frac{x}{y}\right|\right)}^{\frac{3}{2}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|\]
\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}} + \left|\frac{z}{t}\right| \cdot \left|\frac{z}{t}\right|
double f(double x, double y, double z, double t) {
        double r664967 = x;
        double r664968 = r664967 * r664967;
        double r664969 = y;
        double r664970 = r664969 * r664969;
        double r664971 = r664968 / r664970;
        double r664972 = z;
        double r664973 = r664972 * r664972;
        double r664974 = t;
        double r664975 = r664974 * r664974;
        double r664976 = r664973 / r664975;
        double r664977 = r664971 + r664976;
        return r664977;
}
↓
double f(double x, double y, double z, double t) {
        double r664978 = x;
        double r664979 = y;
        double r664980 = r664978 / r664979;
        double r664981 = fabs(r664980);
        double r664982 = sqrt(r664981);
        double r664983 = 1.5;
        double r664984 = pow(r664981, r664983);
        double r664985 = r664982 * r664984;
        double r664986 = z;
        double r664987 = t;
        double r664988 = r664986 / r664987;
        double r664989 = fabs(r664988);
        double r664990 = r664989 * r664989;
        double r664991 = r664985 + r664990;
        return r664991;
}

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

Original33.9
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.9

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

  3. Applied add-sqr-sqrt34.0

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

  4. Simplified33.9

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

  5. Simplified19.4

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

  7. Applied add-sqr-sqrt19.4

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

  8. Simplified19.4

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

  9. Simplified0.4

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

  11. Applied add-sqr-sqrt0.5

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

  12. Applied associate-*l*0.5

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

  13. Simplified0.5

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

  14. Final simplification0.5

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

Reproduce

herbie shell --seed 2020047 
(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))))