Average Error: 0.2 → 0.1
Time: 3.1s
Precision: binary64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \sqrt[3]{{\left(\frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\right)}^{3}}\]
\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 code(double x) {
	return ((double) (((double) (6.0 * ((double) (x - 1.0)))) / ((double) (((double) (x + 1.0)) + ((double) (4.0 * ((double) sqrt(x))))))));
}
↓
double code(double x) {
	return ((double) (6.0 * ((double) cbrt(((double) pow(((double) (((double) (x - 1.0)) / ((double) (((double) (x + 1.0)) + ((double) (4.0 * ((double) sqrt(x)))))))), 3.0))))));
}

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 *-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-cube20.8

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

  8. Applied add-cbrt-cube21.4

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

  9. Applied cbrt-undiv21.4

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

  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 2020162 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :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)))))