Average Error: 0.2 → 0.2
Time: 16.6s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{1}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \cdot \sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}} \cdot \frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{1}{\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}}} \cdot \frac{6}{\sqrt[3]{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}
double f(double x) {
        double r567757 = 6.0;
        double r567758 = x;
        double r567759 = 1.0;
        double r567760 = r567758 - r567759;
        double r567761 = r567757 * r567760;
        double r567762 = r567758 + r567759;
        double r567763 = 4.0;
        double r567764 = sqrt(r567758);
        double r567765 = r567763 * r567764;
        double r567766 = r567762 + r567765;
        double r567767 = r567761 / r567766;
        return r567767;
}
↓
double f(double x) {
        double r567768 = 1.0;
        double r567769 = x;
        double r567770 = 1.0;
        double r567771 = r567769 + r567770;
        double r567772 = 4.0;
        double r567773 = sqrt(r567769);
        double r567774 = r567772 * r567773;
        double r567775 = r567771 + r567774;
        double r567776 = r567769 - r567770;
        double r567777 = r567775 / r567776;
        double r567778 = cbrt(r567777);
        double r567779 = r567778 * r567778;
        double r567780 = r567768 / r567779;
        double r567781 = 6.0;
        double r567782 = r567781 / r567778;
        double r567783 = r567780 * r567782;
        return r567783;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.2
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
  2. 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-cbrt0.2

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

  6. Applied *-un-lft-identity0.2

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

  7. Applied times-frac0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 
(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)))))