mish

std.elementwise.mish · Level L1

Mish: x · tanh(softplus(x)). Calls softplus.

x·tanh(softplus(x))

Signature

mish(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]softplusspTanhtMultiplyyyf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference x * np.tanh(np.log(1 + np.exp(x))) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 144 float64 results inside the running error bound; the closest uses 90% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
52%
bit-equal to the NumPy formula in float64
94%
largest error, in units in the last place
2.0e+3

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls
softplus
Called by
—
sha256:7665a8521240fa5e1c170971a88e4591b88ebd0ed7134126924bb03b1fbb851e

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.mish · Ω:mish
Pins
sha256:e7ab6ed2b8b90fdea99976beae607f6cdbc65942d6f08e0ebf5927d9e608e0d0this graph and the 2 it reaches through calls
Evidence
sha256:cc78f85afc52a5833a4f8b288dc99dcac06164905cd3c51cbdc6b831329b59fbthe 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.