Average Error: 0.2 → 0.0
Time: 12.0s
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 r661678 = 6.0;
        double r661679 = x;
        double r661680 = 1.0;
        double r661681 = r661679 - r661680;
        double r661682 = r661678 * r661681;
        double r661683 = r661679 + r661680;
        double r661684 = 4.0;
        double r661685 = sqrt(r661679);
        double r661686 = r661684 * r661685;
        double r661687 = r661683 + r661686;
        double r661688 = r661682 / r661687;
        return r661688;
}
↓
double f(double x) {
        double r661689 = 6.0;
        double r661690 = x;
        double r661691 = 1.0;
        double r661692 = r661690 - r661691;
        double r661693 = r661690 + r661691;
        double r661694 = 4.0;
        double r661695 = sqrt(r661690);
        double r661696 = r661694 * r661695;
        double r661697 = r661693 + r661696;
        double r661698 = r661692 / r661697;
        double r661699 = r661689 * r661698;
        return r661699;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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 2019306 
(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)))))