softsign

std.elementwise.softsign · Level L0

Softsign: a smooth, bounded alternative to tanh. Calls abs.

x / (1 + |x|)

Signature

softsign(x: f64[n]) → f64[n]

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.

xf64[n]1.0absaxAdddenDivideyyf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference x / (1 + np.abs(x)) in exact rational arithmetic, on all 40 test cases.
  • All 154 float64 results inside the running error bound; the closest uses 85% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
94%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.92

Identity

Calls
abs
Called by
—
sha256:dc77da571580ff51828de0ee57eebdc482b7651967852af989afa23b677c4e81

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

Control handle

Symbol
Ω:std.elementwise.softsign · Ω:softsign
Pins
sha256:d9f18b790f4d70bad5dd88520e0342af6a8f8d698386dd5bc69218dc71239014this graph and the 1 it reaches through calls
Evidence
sha256:0c916289cc59065255b915177ec00f1a847404afa7014753149e8f1658d3f2bethe 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.