Average Error: 0.2 → 0.0
Time: 11.0s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \cdot 6
double f(double x) {
        double r640703 = 6.0;
        double r640704 = x;
        double r640705 = 1.0;
        double r640706 = r640704 - r640705;
        double r640707 = r640703 * r640706;
        double r640708 = r640704 + r640705;
        double r640709 = 4.0;
        double r640710 = sqrt(r640704);
        double r640711 = r640709 * r640710;
        double r640712 = r640708 + r640711;
        double r640713 = r640707 / r640712;
        return r640713;
}
↓
double f(double x) {
        double r640714 = x;
        double r640715 = 1.0;
        double r640716 = r640714 - r640715;
        double r640717 = r640714 + r640715;
        double r640718 = 4.0;
        double r640719 = sqrt(r640714);
        double r640720 = r640718 * r640719;
        double r640721 = r640717 + r640720;
        double r640722 = r640716 / r640721;
        double r640723 = 6.0;
        double r640724 = r640722 * r640723;
        return r640724;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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. Using strategy rm

  7. Applied *-commutative0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 
(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)))))