Average Error: 0.2 → 0.1
Time: 12.8s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{\frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{\frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}
double f(double x) {
        double r569695 = 6.0;
        double r569696 = x;
        double r569697 = 1.0;
        double r569698 = r569696 - r569697;
        double r569699 = r569695 * r569698;
        double r569700 = r569696 + r569697;
        double r569701 = 4.0;
        double r569702 = sqrt(r569696);
        double r569703 = r569701 * r569702;
        double r569704 = r569700 + r569703;
        double r569705 = r569699 / r569704;
        return r569705;
}
↓
double f(double x) {
        double r569706 = 6.0;
        double r569707 = x;
        double r569708 = 1.0;
        double r569709 = r569707 + r569708;
        double r569710 = 4.0;
        double r569711 = sqrt(r569707);
        double r569712 = r569710 * r569711;
        double r569713 = r569709 + r569712;
        double r569714 = r569707 - r569708;
        double r569715 = r569713 / r569714;
        double r569716 = cbrt(r569715);
        double r569717 = r569716 * r569716;
        double r569718 = r569706 / r569717;
        double r569719 = r569718 / r569716;
        return r569719;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
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*0.0

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

  5. Applied add-cube-cbrt0.1

    \[\leadsto \frac{6}{\color{blue}{\left(\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\right) \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}\]

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]

Reproduce

herbie shell --seed 2019326 
(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)))))