Average Error: 0.2 → 0.8
Time: 3.2s
Precision: binary64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{\frac{x}{\sqrt{1 + \sqrt{x + 1}}}}{\sqrt{1 + \sqrt{x + 1}}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{\frac{x}{\sqrt{1 + \sqrt{x + 1}}}}{\sqrt{1 + \sqrt{x + 1}}}
double code(double x) {
	return ((double) (x / ((double) (1.0 + ((double) sqrt(((double) (x + 1.0))))))));
}
↓
double code(double x) {
	return ((double) (((double) (x / ((double) sqrt(((double) (1.0 + ((double) sqrt(((double) (x + 1.0)))))))))) / ((double) sqrt(((double) (1.0 + ((double) sqrt(((double) (x + 1.0))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x}{1 + \sqrt{x + 1}}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt1.1

    \[\leadsto \frac{x}{\color{blue}{\sqrt{1 + \sqrt{x + 1}} \cdot \sqrt{1 + \sqrt{x + 1}}}}\]

  4. Applied associate-/r*0.8

    \[\leadsto \color{blue}{\frac{\frac{x}{\sqrt{1 + \sqrt{x + 1}}}}{\sqrt{1 + \sqrt{x + 1}}}}\]

  5. Final simplification0.8

    \[\leadsto \frac{\frac{x}{\sqrt{1 + \sqrt{x + 1}}}}{\sqrt{1 + \sqrt{x + 1}}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))