Average Error: 0.2 → 0.1
Time: 8.0s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{1}{\frac{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}{6}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{1}{\frac{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}{6}}
double f(double x) {
        double r872929 = 6.0;
        double r872930 = x;
        double r872931 = 1.0;
        double r872932 = r872930 - r872931;
        double r872933 = r872929 * r872932;
        double r872934 = r872930 + r872931;
        double r872935 = 4.0;
        double r872936 = sqrt(r872930);
        double r872937 = r872935 * r872936;
        double r872938 = r872934 + r872937;
        double r872939 = r872933 / r872938;
        return r872939;
}
↓
double f(double x) {
        double r872940 = 1.0;
        double r872941 = x;
        double r872942 = 1.0;
        double r872943 = r872941 + r872942;
        double r872944 = 4.0;
        double r872945 = sqrt(r872941);
        double r872946 = r872944 * r872945;
        double r872947 = r872943 + r872946;
        double r872948 = r872941 - r872942;
        double r872949 = r872947 / r872948;
        double r872950 = 6.0;
        double r872951 = r872949 / r872950;
        double r872952 = r872940 / r872951;
        return r872952;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.1
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]
  4. Using strategy rm

  5. Applied clear-num0.1

    \[\leadsto \color{blue}{\frac{1}{\frac{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}{6}}}\]

  6. Final simplification0.1

    \[\leadsto \frac{1}{\frac{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}{6}}\]

Reproduce

herbie shell --seed 2020018 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :herbie-target
  (/ 6 (/ (+ (+ x 1) (* 4 (sqrt x))) (- x 1)))

  (/ (* 6 (- x 1)) (+ (+ x 1) (* 4 (sqrt x)))))