Average Error: 30.8 → 30.8
Time: 906.0ms
Precision: binary64
\[\sqrt{x \cdot x + 1} - 1\]
↓
\[\sqrt{x \cdot x + 1} - 1\]
\sqrt{x \cdot x + 1} - 1
↓
\sqrt{x \cdot x + 1} - 1
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) + 1.0)))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (x * x)) + 1.0)))) - 1.0));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.8

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

  2. Final simplification30.8

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

Reproduce

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