Average Error: 0.2 → 0.0
Time: 3.1s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
double f(double x) {
        double r981857 = 6.0;
        double r981858 = x;
        double r981859 = 1.0;
        double r981860 = r981858 - r981859;
        double r981861 = r981857 * r981860;
        double r981862 = r981858 + r981859;
        double r981863 = 4.0;
        double r981864 = sqrt(r981858);
        double r981865 = r981863 * r981864;
        double r981866 = r981862 + r981865;
        double r981867 = r981861 / r981866;
        return r981867;
}
↓
double f(double x) {
        double r981868 = 6.0;
        double r981869 = x;
        double r981870 = 1.0;
        double r981871 = r981869 - r981870;
        double r981872 = r981869 + r981870;
        double r981873 = 4.0;
        double r981874 = sqrt(r981869);
        double r981875 = r981873 * r981874;
        double r981876 = r981872 + r981875;
        double r981877 = r981871 / r981876;
        double r981878 = r981868 * r981877;
        return r981878;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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 *-un-lft-identity0.2

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

  4. Applied times-frac0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 
(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)))))