Average Error: 33.8 → 0.5
Time: 18.1s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{x}{y} \cdot \frac{x}{y} + \sqrt{\left|\frac{z}{t}\right|} \cdot \left(\sqrt{\left|\frac{z}{t}\right|} \cdot \left|\frac{z}{t}\right|\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{x}{y} \cdot \frac{x}{y} + \sqrt{\left|\frac{z}{t}\right|} \cdot \left(\sqrt{\left|\frac{z}{t}\right|} \cdot \left|\frac{z}{t}\right|\right)
double f(double x, double y, double z, double t) {
        double r440020 = x;
        double r440021 = r440020 * r440020;
        double r440022 = y;
        double r440023 = r440022 * r440022;
        double r440024 = r440021 / r440023;
        double r440025 = z;
        double r440026 = r440025 * r440025;
        double r440027 = t;
        double r440028 = r440027 * r440027;
        double r440029 = r440026 / r440028;
        double r440030 = r440024 + r440029;
        return r440030;
}
↓
double f(double x, double y, double z, double t) {
        double r440031 = x;
        double r440032 = y;
        double r440033 = r440031 / r440032;
        double r440034 = r440033 * r440033;
        double r440035 = z;
        double r440036 = t;
        double r440037 = r440035 / r440036;
        double r440038 = fabs(r440037);
        double r440039 = sqrt(r440038);
        double r440040 = r440039 * r440038;
        double r440041 = r440039 * r440040;
        double r440042 = r440034 + r440041;
        return r440042;
}

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

Original33.8
Target0.4
Herbie0.5
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.8

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

  3. Applied add-sqr-sqrt33.8

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

  4. Simplified33.8

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

  5. Simplified19.4

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

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

  10. Applied associate-*l*0.5

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

  11. Simplified0.6

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

  13. Applied cube-mult0.6

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

  14. Simplified0.5

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

  15. Final simplification0.5

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

Reproduce

herbie shell --seed 2019305 
(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))))