telescoping_sum
std.seq.telescoping_sum · Level L2The telescoping sum Σ_{k=0}^{N−1} (b_k − b_{k+1}) = b_0 − b_N of a sequence b_0 … b_N: every inner term cancels. The infinite series converges exactly when b_N has a limit, to b_0 − lim b_N.
Σ (b_k − b_{k+1}) = b_0 − b_N
Signature
telescoping_sum(bseq: f64[n]) → f64[]
Structure
The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.
- input
- operation
- constant
- call
- output
Verification
- Signature proven by NOVA’s shape solver, for every size.
- Equal to the reference
sum of b[k] − b[k+1]in exact rational arithmetic, on all 40 test cases. - All 40 float64 results inside the running error bound; the closest uses 64% of it.
- Interpreter and NumPy backend return bit-identical results.
- At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 80% of it.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 100%
- bit-equal to the NumPy formula in float64
- 83%
- largest error, in units in the last place
- 0.50
Identity
Calls
—
Called by
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sha256:04c8bcd931a02339e06c192f46cb2bea1e595a9a0dcb8eb9cbcde57cec490c97The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.seq.telescoping_sum · Ω:telescoping_sum
- Pins
sha256:7443ce99a10c9e5feb24d380123d6ec1487a13b38ad4a172dc7d749dac14756bthis graph alone- Evidence
sha256:5e52b2a2726dc93a6631509ae0773554fd9a0b09cec88a38f2ed2aaec45aeba0the hash of its verification record- Needs
- no capability: a pure function
Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.