mse

std.loss.mse · Level L0

Mean squared error.

(1/n)·Σᵢ (yᵢ − tᵢ)²

Signature

mse(y: f64[n], t: 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 a call to another library function; select it to open that function.

yf64[n]tf64[n]SubtractdMultiplyddMeanllf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.mean((y - t) ** 2) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 30% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
78%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.51

Identity

Calls
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Called by
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sha256:beb47019027c534e6e3fdb812e6f289ba99bb5c636648b5701afb7b648d60bd6

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.