Average Error: 0.2 → 0.0
Time: 10.1s
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 r45665936 = 6.0;
        double r45665937 = x;
        double r45665938 = 1.0;
        double r45665939 = r45665937 - r45665938;
        double r45665940 = r45665936 * r45665939;
        double r45665941 = r45665937 + r45665938;
        double r45665942 = 4.0;
        double r45665943 = sqrt(r45665937);
        double r45665944 = r45665942 * r45665943;
        double r45665945 = r45665941 + r45665944;
        double r45665946 = r45665940 / r45665945;
        return r45665946;
}
↓
double f(double x) {
        double r45665947 = 6.0;
        double r45665948 = x;
        double r45665949 = 1.0;
        double r45665950 = r45665948 + r45665949;
        double r45665951 = 4.0;
        double r45665952 = sqrt(r45665948);
        double r45665953 = r45665951 * r45665952;
        double r45665954 = r45665950 + r45665953;
        double r45665955 = r45665948 - r45665949;
        double r45665956 = r45665954 / r45665955;
        double r45665957 = r45665947 / r45665956;
        return r45665957;
}

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 2019171 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))