why does quad() care about scaling?

[William Crutchfield]

mpm.quad(lambda t: mpm.sin(t) * 1.e40, [1, 3], verbose=True)

Integrating from 1 to 3 (degree 1 of 8) Integrating from 1 to 3 (degree 2 of 8) Estimated error: 6.16112e+36 epsilon: 2.18953e-47 result: 1.53029e+40 Integrating from 1 to 3 (degree 3 of 8) Estimated error: 1.0 epsilon: 2.18953e-47 result: 1.53029e+40 Integrating from 1 to 3 (degree 4 of 8) Estimated error: 1.0 epsilon: 2.18953e-47 result: 1.53029e+40 Integrating from 1 to 3 (degree 5 of 8) Estimated error: 1.0 epsilon: 2.18953e-47 result: 1.53029e+40 Integrating from 1 to 3 (degree 6 of 8) Estimated error: 1.0e-10 epsilon: 2.18953e-47 result: 1.53029e+40 Integrating from 1 to 3 (degree 7 of 8) Estimated error: 1.0e-9 epsilon: 2.18953e-47 result: 1.53029e+40 Integrating from 1 to 3 (degree 8 of 8) Estimated error: 1.0e-10 epsilon: 2.18953e-47 result: 1.53029e+40 Failed to reach full accuracy. Estimated error: 1.0e-10

Needless to say, without the 1.e40 scaling quad() does hit full accuracy.

Is quad() iterating until it hits an absolute error target rather than

a relative error target?

[Sergey B Kirpichev]

On Fri, Jan 09, 2026 at 01:28:55PM -0800, William Crutchfield wrote:
> Is quad() iterating until it hits an absolute error target rather than
> a relative error target?

See QuadratureRule.estimate_error().