Average Error: 30.0 → 30.0
Time: 664.0ms
Precision: binary64
Cost: 13120
\[\sqrt{x + 1} - \sqrt{x}\]
↓
\[\sqrt{x + 1} - \sqrt{x}\]
\sqrt{x + 1} - \sqrt{x}
↓
\sqrt{x + 1} - \sqrt{x}
(FPCore (x) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))
↓
(FPCore (x) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))
double code(double x) {
	return sqrt(x + 1.0) - sqrt(x);
}
↓
double code(double x) {
	return sqrt(x + 1.0) - sqrt(x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.0
Target0.2
Herbie30.0
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]

Derivation

  1. Initial program 30.0

    \[\sqrt{x + 1} - \sqrt{x}\]

Reproduce

herbie shell --seed 2021042 
(FPCore (x)
  :name "2sqrt (example 3.1)"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

  (- (sqrt (+ x 1.0)) (sqrt x)))