Average Error: 34.3 → 0.6
Time: 3.3s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
{\left(\sqrt{\left|\frac{x}{y}\right|}\right)}^{3} \cdot \sqrt{\left|\frac{x}{y}\right|} + \frac{z}{t} \cdot \frac{z}{t}
double f(double x, double y, double z, double t) {
        double r658025 = x;
        double r658026 = r658025 * r658025;
        double r658027 = y;
        double r658028 = r658027 * r658027;
        double r658029 = r658026 / r658028;
        double r658030 = z;
        double r658031 = r658030 * r658030;
        double r658032 = t;
        double r658033 = r658032 * r658032;
        double r658034 = r658031 / r658033;
        double r658035 = r658029 + r658034;
        return r658035;
}
↓
double f(double x, double y, double z, double t) {
        double r658036 = x;
        double r658037 = y;
        double r658038 = r658036 / r658037;
        double r658039 = fabs(r658038);
        double r658040 = sqrt(r658039);
        double r658041 = 3.0;
        double r658042 = pow(r658040, r658041);
        double r658043 = r658042 * r658040;
        double r658044 = z;
        double r658045 = t;
        double r658046 = r658044 / r658045;
        double r658047 = r658046 * r658046;
        double r658048 = r658043 + r658047;
        return r658048;
}

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

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 times-frac19.5

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

  5. Applied add-sqr-sqrt19.5

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

  6. Simplified19.5

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

  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

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2020036 
(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))))