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Can someone explain why sqrt(x+1) - sqrt(x) is “inaccurate” for all x>1? Inaccurate how, and why, and why is 1/(…) any better? Thanks.
by russfink 1y ago
Can someone explain why sqrt(x+1) - sqrt(x) is “inaccurate” for all x>1? Inaccurate how, and why, and why is 1/(…) any better? Thanks.
- Piezoid 1y agoClose floating-point subtraction loses precision: when x >> 1, sqrt(x+1) ≈ sqrt(x), so their difference suffers cancellation and end up rounding to zero. In contrast, sqrt(x+1) + sqrt(x) approaches 2*sqrt(x) smoothly.