erfc

erfc(x): number

Defined in: packages/math-analysis/src/erfc.ts:33

The complementary error function erfc(x) = 1 − erf(x) — how much of a bell curve lies beyond a given distance from its centre.

This is the one you want for a tail probability, a p-value, or any “how unlikely is this?” question. It is not a convenience wrapper: computing it as 1 - erf(x) loses the entire answer once erf(x) rounds to 1, from about x = 6. Computed directly, it keeps full relative precision down to the underflow limit near x = 26.5, which is what makes a normal tail probability of 1e-100 computable at all.

The rule generalises across this package: reach for the upper form when the answer is small.

O(1) time, O(1) memory in the sense that matters to a caller: the underlying expansion is iterative but bounded, and allocates nothing.

Parameters

x

number

Any real.

Returns

number

erfc(x), in [0, 2].

Example

  erfc(6); // 2.1519736712498916e-17
  1 - erf(6); // 0 — the same quantity, computed the wrong way
  erfc(20); // 5.395865611607905e-176
  ```;

## See

 - [erf](erf.md) when the answer is near 0 rather than near 1.
 - [The error function](https://anthochamp.pages.grenadine.io/node-essentials/topics/math/functions/error-functions/)