Average Error: 0.2 → 0.0
Time: 9.0s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}
double f(double x) {
        double r914982 = 6.0;
        double r914983 = x;
        double r914984 = 1.0;
        double r914985 = r914983 - r914984;
        double r914986 = r914982 * r914985;
        double r914987 = r914983 + r914984;
        double r914988 = 4.0;
        double r914989 = sqrt(r914983);
        double r914990 = r914988 * r914989;
        double r914991 = r914987 + r914990;
        double r914992 = r914986 / r914991;
        return r914992;
}
↓
double f(double x) {
        double r914993 = 6.0;
        double r914994 = x;
        double r914995 = 1.0;
        double r914996 = r914994 + r914995;
        double r914997 = 4.0;
        double r914998 = sqrt(r914994);
        double r914999 = r914997 * r914998;
        double r915000 = r914996 + r914999;
        double r915001 = r914994 - r914995;
        double r915002 = r915000 / r915001;
        double r915003 = r914993 / r915002;
        return r915003;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))))