Average Error: 0.2 → 0.1
Time: 14.9s
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 r618997 = 6.0;
        double r618998 = x;
        double r618999 = 1.0;
        double r619000 = r618998 - r618999;
        double r619001 = r618997 * r619000;
        double r619002 = r618998 + r618999;
        double r619003 = 4.0;
        double r619004 = sqrt(r618998);
        double r619005 = r619003 * r619004;
        double r619006 = r619002 + r619005;
        double r619007 = r619001 / r619006;
        return r619007;
}
↓
double f(double x) {
        double r619008 = 1.0;
        double r619009 = x;
        double r619010 = 1.0;
        double r619011 = r619009 + r619010;
        double r619012 = 4.0;
        double r619013 = sqrt(r619009);
        double r619014 = r619012 * r619013;
        double r619015 = r619011 + r619014;
        double r619016 = r619009 - r619010;
        double r619017 = r619015 / r619016;
        double r619018 = 6.0;
        double r619019 = r619017 / r619018;
        double r619020 = r619008 / r619019;
        return r619020;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
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*0.0

    \[\leadsto \color{blue}{\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]
  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 2019212 
(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)))))