Average Error: 0.2 → 0.0
Time: 3.7s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}
double f(double x) {
        double r945862 = 6.0;
        double r945863 = x;
        double r945864 = 1.0;
        double r945865 = r945863 - r945864;
        double r945866 = r945862 * r945865;
        double r945867 = r945863 + r945864;
        double r945868 = 4.0;
        double r945869 = sqrt(r945863);
        double r945870 = r945868 * r945869;
        double r945871 = r945867 + r945870;
        double r945872 = r945866 / r945871;
        return r945872;
}
↓
double f(double x) {
        double r945873 = 6.0;
        double r945874 = x;
        double r945875 = 1.0;
        double r945876 = r945874 + r945875;
        double r945877 = 4.0;
        double r945878 = sqrt(r945874);
        double r945879 = r945877 * r945878;
        double r945880 = r945876 + r945879;
        double r945881 = r945874 - r945875;
        double r945882 = r945880 / r945881;
        double r945883 = r945873 / r945882;
        return r945883;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

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*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))))