Average Error: 0.2 → 0.0
Time: 7.3s
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 r1128951 = 6.0;
        double r1128952 = x;
        double r1128953 = 1.0;
        double r1128954 = r1128952 - r1128953;
        double r1128955 = r1128951 * r1128954;
        double r1128956 = r1128952 + r1128953;
        double r1128957 = 4.0;
        double r1128958 = sqrt(r1128952);
        double r1128959 = r1128957 * r1128958;
        double r1128960 = r1128956 + r1128959;
        double r1128961 = r1128955 / r1128960;
        return r1128961;
}
↓
double f(double x) {
        double r1128962 = 6.0;
        double r1128963 = x;
        double r1128964 = 1.0;
        double r1128965 = r1128963 + r1128964;
        double r1128966 = 4.0;
        double r1128967 = sqrt(r1128963);
        double r1128968 = r1128966 * r1128967;
        double r1128969 = r1128965 + r1128968;
        double r1128970 = r1128963 - r1128964;
        double r1128971 = r1128969 / r1128970;
        double r1128972 = r1128962 / r1128971;
        return r1128972;
}

Error

Bits error versus x

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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)))))