Average Error: 0.3 → 0.0
Time: 3.3s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \cdot 6
double f(double x) {
        double r832839 = 6.0;
        double r832840 = x;
        double r832841 = 1.0;
        double r832842 = r832840 - r832841;
        double r832843 = r832839 * r832842;
        double r832844 = r832840 + r832841;
        double r832845 = 4.0;
        double r832846 = sqrt(r832840);
        double r832847 = r832845 * r832846;
        double r832848 = r832844 + r832847;
        double r832849 = r832843 / r832848;
        return r832849;
}
↓
double f(double x) {
        double r832850 = x;
        double r832851 = 1.0;
        double r832852 = r832850 - r832851;
        double r832853 = r832850 + r832851;
        double r832854 = 4.0;
        double r832855 = sqrt(r832850);
        double r832856 = r832854 * r832855;
        double r832857 = r832853 + r832856;
        double r832858 = r832852 / r832857;
        double r832859 = 6.0;
        double r832860 = r832858 * r832859;
        return r832860;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.1
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.3

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

  3. Applied *-un-lft-identity0.3

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

  4. Applied times-frac0.0

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

  5. Simplified0.0

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

  7. Applied *-commutative0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 
(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)))))