Average Error: 0.2 → 0.1
Time: 2.7s
Precision: binary64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \sqrt[3]{{\left(\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}\right)}^{3}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \sqrt[3]{{\left(\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}\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) (x + ((double) (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
Target0.1
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. Simplified0.0

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

  4. Applied add-cbrt-cube20.8

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

  5. Applied add-cbrt-cube20.7

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

  6. Applied cbrt-undiv20.7

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020184 
(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)))))