From ec05e29ef9c84296cc15b9433c9dd59c5244791e Mon Sep 17 00:00:00 2001 From: Vectornaut Date: Sat, 10 Feb 2024 19:23:31 +0000 Subject: [PATCH] Discuss hyperplane hit rate with and without scale constraint --- Engine-prototype.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/Engine-prototype.md b/Engine-prototype.md index f5a0850..10cca17 100644 --- a/Engine-prototype.md +++ b/Engine-prototype.md @@ -2,7 +2,8 @@ * Cutting along a hyperplane with real coefficients and offset has been doing a good job of finding real solutions. * Hyperplanes that go through the origin has been performing better than hyperplanes with other offsets. * Ones that go through the trivial solution seem the worst. - * In tests based on commit 8e33987, hyperplanes through the origin tend to hit around 1.5 times as many real solutions as ones through the trivial solution. + * In tests with no scale constraint (based on commit 8e33987), hyperplanes through the origin tend to hit around 1.5 times as many real solutions as ones through the trivial solution. + * In tests with a scale constraint (based on commit af1d31f), the hit ratio drops to 1.0 to 1.2, and becomes more variable. ## Rational points