Average Error: 0.2 → 0.3
Time: 8.5s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\sqrt{\left(x + 1\right) + 4 \cdot \sqrt{x}}} \cdot \frac{x - 1}{\sqrt{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\sqrt{\left(x + 1\right) + 4 \cdot \sqrt{x}}} \cdot \frac{x - 1}{\sqrt{\left(x + 1\right) + 4 \cdot \sqrt{x}}}
double f(double x) {
        double r4981 = 6.0;
        double r4982 = x;
        double r4983 = 1.0;
        double r4984 = r4982 - r4983;
        double r4985 = r4981 * r4984;
        double r4986 = r4982 + r4983;
        double r4987 = 4.0;
        double r4988 = sqrt(r4982);
        double r4989 = r4987 * r4988;
        double r4990 = r4986 + r4989;
        double r4991 = r4985 / r4990;
        return r4991;
}
↓
double f(double x) {
        double r4992 = 6.0;
        double r4993 = x;
        double r4994 = 1.0;
        double r4995 = r4993 + r4994;
        double r4996 = 4.0;
        double r4997 = sqrt(r4993);
        double r4998 = r4996 * r4997;
        double r4999 = r4995 + r4998;
        double r5000 = sqrt(r4999);
        double r5001 = r4992 / r5000;
        double r5002 = r4993 - r4994;
        double r5003 = r5002 / r5000;
        double r5004 = r5001 * r5003;
        return r5004;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.3
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

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 add-sqr-sqrt0.4

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

  4. Applied times-frac0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020025 
(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)))))