Average Error: 0.7 → 0.7
Time: 1.1s
Precision: binary64
\[\frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}}\]
↓
\[\frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}}\]
\frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}}
↓
\frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}}
double code(double x) {
	return ((double) (1.0 / ((double) (((double) (((double) (x + 1.0)) * ((double) sqrt(x)))) + ((double) (x * ((double) sqrt(((double) (x + 1.0))))))))));
}
↓
double code(double x) {
	return ((double) (1.0 / ((double) (((double) (((double) (x + 1.0)) * ((double) sqrt(x)))) + ((double) (x * ((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 0.7

    \[\frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}}\]

  2. Final simplification0.7

    \[\leadsto \frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ 1 (+ (* (+ x 1) (sqrt x)) (* x (sqrt (+ x 1)))))"
  :precision binary64
  (/ 1.0 (+ (* (+ x 1.0) (sqrt x)) (* x (sqrt (+ x 1.0))))))