Average Error: 0.2 → 0.3
Time: 4.6s
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 r1104737 = 6.0;
        double r1104738 = x;
        double r1104739 = 1.0;
        double r1104740 = r1104738 - r1104739;
        double r1104741 = r1104737 * r1104740;
        double r1104742 = r1104738 + r1104739;
        double r1104743 = 4.0;
        double r1104744 = sqrt(r1104738);
        double r1104745 = r1104743 * r1104744;
        double r1104746 = r1104742 + r1104745;
        double r1104747 = r1104741 / r1104746;
        return r1104747;
}
↓
double f(double x) {
        double r1104748 = 6.0;
        double r1104749 = x;
        double r1104750 = 1.0;
        double r1104751 = r1104749 + r1104750;
        double r1104752 = 4.0;
        double r1104753 = sqrt(r1104749);
        double r1104754 = r1104752 * r1104753;
        double r1104755 = r1104751 + r1104754;
        double r1104756 = sqrt(r1104755);
        double r1104757 = r1104748 / r1104756;
        double r1104758 = r1104749 - r1104750;
        double r1104759 = r1104758 / r1104756;
        double r1104760 = r1104757 * r1104759;
        return r1104760;
}

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)))))