Average Error: 0.2 → 0.2
Time: 14.6s
Precision: 64
\[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}} \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}}\]
\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}
↓
\left(\sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}} \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}}
double f(double x) {
        double r48240539 = 6.0;
        double r48240540 = x;
        double r48240541 = 1.0;
        double r48240542 = r48240540 - r48240541;
        double r48240543 = r48240539 * r48240542;
        double r48240544 = r48240540 + r48240541;
        double r48240545 = 4.0;
        double r48240546 = sqrt(r48240540);
        double r48240547 = r48240545 * r48240546;
        double r48240548 = r48240544 + r48240547;
        double r48240549 = r48240543 / r48240548;
        return r48240549;
}
↓
double f(double x) {
        double r48240550 = x;
        double r48240551 = 1.0;
        double r48240552 = r48240550 - r48240551;
        double r48240553 = 6.0;
        double r48240554 = r48240552 * r48240553;
        double r48240555 = r48240550 + r48240551;
        double r48240556 = sqrt(r48240550);
        double r48240557 = 4.0;
        double r48240558 = r48240556 * r48240557;
        double r48240559 = r48240555 + r48240558;
        double r48240560 = r48240554 / r48240559;
        double r48240561 = r48240560 * r48240560;
        double r48240562 = r48240560 * r48240561;
        double r48240563 = cbrt(r48240562);
        double r48240564 = cbrt(r48240563);
        double r48240565 = r48240564 * r48240564;
        double r48240566 = r48240565 * r48240564;
        return r48240566;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.2
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube1.1

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}} \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\right) \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\sqrt[3]{\left(\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}} \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\right) \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}}} \cdot \sqrt[3]{\sqrt[3]{\left(\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}} \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\right) \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}}}\right) \cdot \sqrt[3]{\sqrt[3]{\left(\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}} \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\right) \cdot \frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}}}}\]

  6. Final simplification0.2

    \[\leadsto \left(\sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}} \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \left(\frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0} \cdot \frac{\left(x - 1.0\right) \cdot 6.0}{\left(x + 1.0\right) + \sqrt{x} \cdot 4.0}\right)}}\]

Reproduce

herbie shell --seed 2019163 
(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)))))