Average Error: 0.2 → 0.2
Time: 12.3s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
double f(double x) {
        double r701784 = 6.0;
        double r701785 = x;
        double r701786 = 1.0;
        double r701787 = r701785 - r701786;
        double r701788 = r701784 * r701787;
        double r701789 = r701785 + r701786;
        double r701790 = 4.0;
        double r701791 = sqrt(r701785);
        double r701792 = r701790 * r701791;
        double r701793 = r701789 + r701792;
        double r701794 = r701788 / r701793;
        return r701794;
}
↓
double f(double x) {
        double r701795 = 6.0;
        double r701796 = x;
        double r701797 = 1.0;
        double r701798 = r701796 - r701797;
        double r701799 = r701795 * r701798;
        double r701800 = r701796 + r701797;
        double r701801 = 4.0;
        double r701802 = sqrt(r701796);
        double r701803 = r701801 * r701802;
        double r701804 = r701800 + r701803;
        double r701805 = r701799 / r701804;
        return r701805;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019297 
(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)))))