Average Error: 0.2 → 0.0
Time: 4.8s
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 r1034829 = 6.0;
        double r1034830 = x;
        double r1034831 = 1.0;
        double r1034832 = r1034830 - r1034831;
        double r1034833 = r1034829 * r1034832;
        double r1034834 = r1034830 + r1034831;
        double r1034835 = 4.0;
        double r1034836 = sqrt(r1034830);
        double r1034837 = r1034835 * r1034836;
        double r1034838 = r1034834 + r1034837;
        double r1034839 = r1034833 / r1034838;
        return r1034839;
}
↓
double f(double x) {
        double r1034840 = 6.0;
        double r1034841 = x;
        double r1034842 = 1.0;
        double r1034843 = r1034841 - r1034842;
        double r1034844 = r1034841 + r1034842;
        double r1034845 = 4.0;
        double r1034846 = sqrt(r1034841);
        double r1034847 = r1034845 * r1034846;
        double r1034848 = r1034844 + r1034847;
        double r1034849 = r1034843 / r1034848;
        double r1034850 = r1034840 * r1034849;
        return r1034850;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020089 
(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)))))