Average Error: 4.2 → 4.2
Time: 928.0ms
Precision: binary64
\[\sqrt{1 + x \cdot x} - \sqrt{1 + x} \cdot x\]
↓
\[\sqrt{1 + x \cdot x} - \sqrt{1 + x} \cdot x\]
\sqrt{1 + x \cdot x} - \sqrt{1 + x} \cdot x
↓
\sqrt{1 + x \cdot x} - \sqrt{1 + x} \cdot x
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) (x * x)))))) - ((double) (((double) sqrt(((double) (1.0 + x)))) * x))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) (x * x)))))) - ((double) (((double) sqrt(((double) (1.0 + x)))) * x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.2

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

  2. Final simplification4.2

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

Reproduce

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