Let Compare and Equals treat float noise as equal numbers

A graph that checks "time - late == 6" after On timer (#224) failed,
because the difference comes out as 5.999999999999972. Both values are
sums of measured frame times, and they round along different paths.
The only workaround was a Round node in front of every comparison.

- New helper nearlyEqual in values.ts. Two numbers count as equal when
  |a - b| <= 1e-9 * max(1, |a|, |b|). The tolerance grows with the
  size of the values, so it holds for hours of summed dt.
- Compare uses the rule for all six operators. "<" and ">" only hold
  when the values are not nearly equal, "<=" and ">=" also hold when
  they are. So "==" and ">" are never true at the same time.
- Equals uses the same rule when both inputs are real numbers. Objects
  still compare by identity, everything else as text. The node
  description says so.
- The tolerance is fixed, there is no parameter on the node. Physics
  values come from float32 in Rapier and are not covered on purpose.
- The log display is unchanged and still prints the raw number.

Tests:
- ./check.sh: 156 files, 2311 tests, CHECK EXIT 0 (before 2300).
- 11 new cases in node-catalog.test.ts, including the value from the
  log against 6, growth with magnitude, 6.001 != 6 and 1e-6 > 0.
- Counter-check exact compare: exactly the 8 noise cases fail.
- Counter-check "<"/">" without the exclusion: exactly 2 cases fail.
- No e2e change, the check sum stays at 1374.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/core/graph/nodes/data/Compare.ts

@@ -1,15 +1,16 @@
 import type { NodeDef } from '../../NodeRegistry';
-import { asNumber } from '../../values';
+import { asNumber, nearlyEqual } from '../../values';
 import { bool, num } from '../shared';
 
 import { textOf } from '../../../model/Properties';
+// All six share one notion of equal, so `==` and `>` are never true at once.
 const OPERATORS: Record<string, (a: number, b: number) => boolean> = {
-  '==': (a, b) => a === b,
+  '==': (a, b) => nearlyEqual(a, b),
-  '!=': (a, b) => a !== b,
+  '!=': (a, b) => !nearlyEqual(a, b),
-  '<': (a, b) => a < b,
+  '<': (a, b) => a < b && !nearlyEqual(a, b),
-  '<=': (a, b) => a <= b,
+  '<=': (a, b) => a < b || nearlyEqual(a, b),
-  '>': (a, b) => a > b,
+  '>': (a, b) => a > b && !nearlyEqual(a, b),
-  '>=': (a, b) => a >= b,
+  '>=': (a, b) => a > b || nearlyEqual(a, b),
 };
 
 export const Compare: NodeDef = {

src/core/graph/nodes/data/Equals.ts

@@ -1,12 +1,13 @@
 import type { NodeDef } from '../../NodeRegistry';
-import { asEntity, asString } from '../../values';
+import { asEntity, asString, nearlyEqual } from '../../values';
 import { any, bool } from '../shared';
 
 export const Equals: NodeDef = {
   type: 'Equals',
   label: 'Equals',
   category: 'data',
-  description: 'Whether two values are the same. Objects compare by identity, everything else as text.',
+  description:
+    'Whether two values are the same. Objects compare by identity, two numbers up to float noise, everything else as text.',
   inputs: [any('a'), any('b')],
   outputs: [bool('result')],
   params: [],
@@ -14,6 +15,9 @@ export const Equals: NodeDef = {
     const a = asEntity(inputs.a);
     const b = asEntity(inputs.b);
     if (a || b) return { outputs: { result: a === b } };
+    if (typeof inputs.a === 'number' && typeof inputs.b === 'number') {
+      return { outputs: { result: nearlyEqual(inputs.a, inputs.b) } };
+    }
     return { outputs: { result: asString(inputs.a) === asString(inputs.b) } };
   },
 };

src/core/graph/values.ts

@@ -25,6 +25,16 @@ export function isEntity(value: Value | undefined): value is EntityHandle {
   return typeof value === 'object' && value !== null && ENTITY_HANDLE in value;
 }
 
+/**
+ * Whether two numbers are the same up to float noise (#224): a relative 1e-9, never less than 1e-9
+ * absolute. `time - late` lands 1e-14 off a whole second, and after hours of summed `dt` the error
+ * still stays far below this, while 6 and 6.001 remain apart.
+ */
+export function nearlyEqual(a: number, b: number): boolean {
+  if (a === b) return true;
+  return Math.abs(a - b) <= 1e-9 * Math.max(1, Math.abs(a), Math.abs(b));
+}
+
 /** A list of anything a data edge carries – a handle among the items is what `isList` cannot say. */
 function isValueList(value: Value | undefined): value is ValueList {
   return Array.isArray(value);

tests/core/node-catalog.test.ts

@@ -685,11 +685,72 @@ const CASES: Record<string, Case[]> = {
     { name: 'equal text', inputs: { a: 'a', b: 'a' }, outputs: { result: true } },
     { name: 'a number equals its text form', inputs: { a: 3, b: '3' }, outputs: { result: true } },
     { name: 'objects compare by identity, not by name', inputs: eqNamesakes(), outputs: { result: false } },
+    {
+      name: 'two numbers ignore float noise',
+      inputs: { a: 5.999999999999972, b: 6 },
+      outputs: { result: true },
+    },
+    { name: 'two numbers still tell 6.001 from 6', inputs: { a: 6.001, b: 6 }, outputs: { result: false } },
   ],
   Compare: [
     { name: 'less than', inputs: { a: 1, b: 2 }, params: { op: '<' }, outputs: { result: true } },
     { name: 'greater or equal', inputs: { a: 2, b: 2 }, params: { op: '>=' }, outputs: { result: true } },
     { name: 'not equal', inputs: { a: 2, b: 2 }, params: { op: '!=' }, outputs: { result: false } },
+    // time - late after 6 s of summed dt (#224): the noise counts as equal under every operator.
+    {
+      name: '== ignores float noise',
+      inputs: { a: 5.999999999999972, b: 6 },
+      params: { op: '==' },
+      outputs: { result: true },
+    },
+    {
+      name: '!= ignores float noise',
+      inputs: { a: 5.999999999999972, b: 6 },
+      params: { op: '!=' },
+      outputs: { result: false },
+    },
+    {
+      name: '< ignores float noise',
+      inputs: { a: 5.999999999999972, b: 6 },
+      params: { op: '<' },
+      outputs: { result: false },
+    },
+    {
+      name: '>= ignores float noise',
+      inputs: { a: 5.999999999999972, b: 6 },
+      params: { op: '>=' },
+      outputs: { result: true },
+    },
+    {
+      name: '> ignores float noise',
+      inputs: { a: 6.000000000000028, b: 6 },
+      params: { op: '>' },
+      outputs: { result: false },
+    },
+    {
+      name: '<= ignores float noise',
+      inputs: { a: 6.000000000000028, b: 6 },
+      params: { op: '<=' },
+      outputs: { result: true },
+    },
+    {
+      name: 'the tolerance grows with the values',
+      inputs: { a: 1e6, b: 1e6 + 1e-4 },
+      params: { op: '==' },
+      outputs: { result: true },
+    },
+    {
+      name: 'a real difference stays one',
+      inputs: { a: 6.001, b: 6 },
+      params: { op: '==' },
+      outputs: { result: false },
+    },
+    {
+      name: 'a tiny value still differs from 0',
+      inputs: { a: 1e-6, b: 0 },
+      params: { op: '>' },
+      outputs: { result: true },
+    },
     {
       name: 'no operator chosen falls back to the default "<"',
       inputs: { a: 1, b: 2 },