Average Error: 0.2 → 0.1
Time: 21.5s
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 r996225 = 6.0;
        double r996226 = x;
        double r996227 = 1.0;
        double r996228 = r996226 - r996227;
        double r996229 = r996225 * r996228;
        double r996230 = r996226 + r996227;
        double r996231 = 4.0;
        double r996232 = sqrt(r996226);
        double r996233 = r996231 * r996232;
        double r996234 = r996230 + r996233;
        double r996235 = r996229 / r996234;
        return r996235;
}
↓
double f(double x) {
        double r996236 = 1.0;
        double r996237 = x;
        double r996238 = 1.0;
        double r996239 = r996237 + r996238;
        double r996240 = 4.0;
        double r996241 = sqrt(r996237);
        double r996242 = r996240 * r996241;
        double r996243 = r996239 + r996242;
        double r996244 = r996237 - r996238;
        double r996245 = r996243 / r996244;
        double r996246 = 6.0;
        double r996247 = r996245 / r996246;
        double r996248 = r996236 / r996247;
        return r996248;
}

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. 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 2020065 
(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)))))