Average Error: 0.2 → 0.1
Time: 13.7s
Precision: 64
\[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
↓
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]
\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}
↓
\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}
double f(double x) {
        double r45037941 = 6.0;
        double r45037942 = x;
        double r45037943 = 1.0;
        double r45037944 = r45037942 - r45037943;
        double r45037945 = r45037941 * r45037944;
        double r45037946 = r45037942 + r45037943;
        double r45037947 = 4.0;
        double r45037948 = sqrt(r45037942);
        double r45037949 = r45037947 * r45037948;
        double r45037950 = r45037946 + r45037949;
        double r45037951 = r45037945 / r45037950;
        return r45037951;
}
↓
double f(double x) {
        double r45037952 = 6.0;
        double r45037953 = x;
        double r45037954 = 1.0;
        double r45037955 = r45037953 + r45037954;
        double r45037956 = 4.0;
        double r45037957 = sqrt(r45037953);
        double r45037958 = r45037956 * r45037957;
        double r45037959 = r45037955 + r45037958;
        double r45037960 = r45037953 - r45037954;
        double r45037961 = r45037959 / r45037960;
        double r45037962 = r45037952 / r45037961;
        return r45037962;
}

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
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Reproduce

herbie shell --seed 2019162 
(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)))))