Average Error: 0.2 → 0.1
Time: 21.6s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}
double f(double x) {
        double r915564 = 6.0;
        double r915565 = x;
        double r915566 = 1.0;
        double r915567 = r915565 - r915566;
        double r915568 = r915564 * r915567;
        double r915569 = r915565 + r915566;
        double r915570 = 4.0;
        double r915571 = sqrt(r915565);
        double r915572 = r915570 * r915571;
        double r915573 = r915569 + r915572;
        double r915574 = r915568 / r915573;
        return r915574;
}
↓
double f(double x) {
        double r915575 = 6.0;
        double r915576 = x;
        double r915577 = 1.0;
        double r915578 = r915576 + r915577;
        double r915579 = 4.0;
        double r915580 = sqrt(r915576);
        double r915581 = r915579 * r915580;
        double r915582 = r915578 + r915581;
        double r915583 = r915576 - r915577;
        double r915584 = r915582 / r915583;
        double r915585 = r915575 / r915584;
        return r915585;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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)))))