Average Error: 0.1 → 0.1
Time: 1.1s
Precision: binary64
\[\sqrt{x + 1} - \sqrt{x} \cdot x\]
↓
\[\sqrt{x + 1} - \sqrt{x} \cdot x\]
\sqrt{x + 1} - \sqrt{x} \cdot x
↓
\sqrt{x + 1} - \sqrt{x} \cdot x
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) (((double) sqrt(x)) * x))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) (((double) sqrt(x)) * x))));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (sqrt (+ x 1)) (* (sqrt x) x))"
  :precision binary64
  (- (sqrt (+ x 1.0)) (* (sqrt x) x)))