Average Error: 0.2 → 0.0
Time: 11.4s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6
double f(double x) {
        double r42020734 = 6.0;
        double r42020735 = x;
        double r42020736 = 1.0;
        double r42020737 = r42020735 - r42020736;
        double r42020738 = r42020734 * r42020737;
        double r42020739 = r42020735 + r42020736;
        double r42020740 = 4.0;
        double r42020741 = sqrt(r42020735);
        double r42020742 = r42020740 * r42020741;
        double r42020743 = r42020739 + r42020742;
        double r42020744 = r42020738 / r42020743;
        return r42020744;
}
↓
double f(double x) {
        double r42020745 = x;
        double r42020746 = 1.0;
        double r42020747 = r42020745 - r42020746;
        double r42020748 = 4.0;
        double r42020749 = sqrt(r42020745);
        double r42020750 = r42020748 * r42020749;
        double r42020751 = r42020745 + r42020746;
        double r42020752 = r42020750 + r42020751;
        double r42020753 = r42020747 / r42020752;
        double r42020754 = 6.0;
        double r42020755 = r42020753 * r42020754;
        return r42020755;
}

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

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))