Average Error: 0.2 → 0.1
Time: 11.8s
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 r919820 = 6.0;
        double r919821 = x;
        double r919822 = 1.0;
        double r919823 = r919821 - r919822;
        double r919824 = r919820 * r919823;
        double r919825 = r919821 + r919822;
        double r919826 = 4.0;
        double r919827 = sqrt(r919821);
        double r919828 = r919826 * r919827;
        double r919829 = r919825 + r919828;
        double r919830 = r919824 / r919829;
        return r919830;
}
↓
double f(double x) {
        double r919831 = 1.0;
        double r919832 = x;
        double r919833 = 1.0;
        double r919834 = r919832 + r919833;
        double r919835 = 4.0;
        double r919836 = sqrt(r919832);
        double r919837 = r919835 * r919836;
        double r919838 = r919834 + r919837;
        double r919839 = r919832 - r919833;
        double r919840 = r919838 / r919839;
        double r919841 = 6.0;
        double r919842 = r919840 / r919841;
        double r919843 = r919831 / r919842;
        return r919843;
}

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 2019209 
(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)))))