Average Error: 0.2 → 0.1
Time: 20.4s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\frac{\left(1 + x\right) + \sqrt{x} \cdot 4}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\frac{\left(1 + x\right) + \sqrt{x} \cdot 4}{x - 1}}
double f(double x) {
        double r44645870 = 6.0;
        double r44645871 = x;
        double r44645872 = 1.0;
        double r44645873 = r44645871 - r44645872;
        double r44645874 = r44645870 * r44645873;
        double r44645875 = r44645871 + r44645872;
        double r44645876 = 4.0;
        double r44645877 = sqrt(r44645871);
        double r44645878 = r44645876 * r44645877;
        double r44645879 = r44645875 + r44645878;
        double r44645880 = r44645874 / r44645879;
        return r44645880;
}
↓
double f(double x) {
        double r44645881 = 6.0;
        double r44645882 = 1.0;
        double r44645883 = x;
        double r44645884 = r44645882 + r44645883;
        double r44645885 = sqrt(r44645883);
        double r44645886 = 4.0;
        double r44645887 = r44645885 * r44645886;
        double r44645888 = r44645884 + r44645887;
        double r44645889 = r44645883 - r44645882;
        double r44645890 = r44645888 / r44645889;
        double r44645891 = r44645881 / r44645890;
        return r44645891;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))