Average Error: 0.2 → 0.1
Time: 4.1s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \sqrt[3]{{\left(\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\right)}^{3}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \sqrt[3]{{\left(\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\right)}^{3}}
double f(double x) {
        double r828626 = 6.0;
        double r828627 = x;
        double r828628 = 1.0;
        double r828629 = r828627 - r828628;
        double r828630 = r828626 * r828629;
        double r828631 = r828627 + r828628;
        double r828632 = 4.0;
        double r828633 = sqrt(r828627);
        double r828634 = r828632 * r828633;
        double r828635 = r828631 + r828634;
        double r828636 = r828630 / r828635;
        return r828636;
}
↓
double f(double x) {
        double r828637 = 6.0;
        double r828638 = x;
        double r828639 = 1.0;
        double r828640 = r828638 - r828639;
        double r828641 = r828638 + r828639;
        double r828642 = 4.0;
        double r828643 = sqrt(r828638);
        double r828644 = r828642 * r828643;
        double r828645 = r828641 + r828644;
        double r828646 = r828640 / r828645;
        double r828647 = 3.0;
        double r828648 = pow(r828646, r828647);
        double r828649 = cbrt(r828648);
        double r828650 = r828637 * r828649;
        return r828650;
}

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 *-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. Using strategy rm

  7. Applied add-cbrt-cube21.3

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

  8. Applied add-cbrt-cube21.9

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

  9. Applied cbrt-undiv21.9

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(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)))))