Hugging Face's logo

Datasets:
roseking
/
openAI-math-dataset

Languages:
English
Chinese
Size:
100K<n<1M
Tags:
mathematics
mirror
lean
formal-proofs
License:
Dataset card Files
xet
 Community
openAI-math-dataset
File size: 14,008 Bytes
e63eb7f
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonLift
import OAI.Combinatorics.EditApproximation.Refinement.StageTerminal
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementSpatial
import OAI.Combinatorics.EditApproximation.Numerics.RationalWideSpatial
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementInvariants
import OAI.Combinatorics.EditApproximation.Refinement.ComputedBandSpacing
import OAI.Combinatorics.EditApproximation.Geometry.UnskippedBands
import OAI.Combinatorics.EditApproximation.Numerics.RationalWideStep
import OAI.Combinatorics.EditApproximation.Refinement.StageComparison
import OAI.Combinatorics.EditApproximation.Geometry.OnlineActionDraw
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonPhysical
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLeaves
import OAI.Combinatorics.EditApproximation.Refinement.ComputedComparisonBand
import OAI.Combinatorics.EditApproximation.Geometry.BandRounding
import OAI.Combinatorics.EditApproximation.Geometry.BandEnvelopes
import OAI.Combinatorics.EditApproximation.Geometry.BandGuards
import OAI.Combinatorics.EditApproximation.Refinement.StageWarmup
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSpatial
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalWarmupSlack
import OAI.Combinatorics.EditApproximation.Geometry.BandParameters
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonBandCoverage
import OAI.Combinatorics.EditApproximation.Geometry.RepresentativeBands
import OAI.Combinatorics.EditApproximation.Geometry.PrefixComparison
import OAI.Combinatorics.EditApproximation.Refinement.ComputedBands
import OAI.Combinatorics.EditApproximation.Geometry.InitialSeedTable
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonParameters
import OAI.Combinatorics.EditApproximation.Numerics.RationalPrefix
import OAI.Combinatorics.EditApproximation.Coarse.CoarseArrayEval
import OAI.Combinatorics.EditApproximation.Coarse.CoarseGlobalSeed
import OAI.Combinatorics.EditApproximation.Geometry.WideBellman
import OAI.Combinatorics.EditApproximation.Geometry.PrefixCosts
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonBounds
import OAI.Combinatorics.EditApproximation.Geometry.StateDomain
import OAI.Combinatorics.EditApproximation.Geometry.SharedActions
import OAI.Combinatorics.EditApproximation.Geometry.SourcePrefixes
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonTree
import OAI.Combinatorics.EditApproximation.Geometry.RoundedComparison
import OAI.Combinatorics.EditApproximation.Refinement.ComputedSeed
import OAI.Combinatorics.EditApproximation.Coarse.CoarseParameters
import OAI.Combinatorics.EditApproximation.Coarse.CoarsePrecision
import OAI.Combinatorics.EditApproximation.Coarse.CoarseInitialWork
import OAI.Combinatorics.EditApproximation.Geometry.Accuracy
import OAI.Combinatorics.EditApproximation.Probability.Amplification
import OAI.Combinatorics.EditApproximation.Geometry.ActionLower
import OAI.Combinatorics.EditApproximation.Geometry.ActionVectors
import OAI.Combinatorics.EditApproximation.Geometry.ActualActionValues
import OAI.Combinatorics.EditApproximation.Geometry.AlignedStates
import OAI.Combinatorics.EditApproximation.Geometry.AlignmentSplitting
import OAI.Combinatorics.EditApproximation.Geometry.Bands
import OAI.Combinatorics.EditApproximation.Geometry.Bellman
import OAI.Combinatorics.EditApproximation.Geometry.BandRegret
import OAI.Combinatorics.EditApproximation.Geometry.BalancedIntervals
import OAI.Combinatorics.EditApproximation.Geometry.BalancedWidths
import OAI.Combinatorics.EditApproximation.Geometry.ChildIncrements
import OAI.Combinatorics.EditApproximation.Coarse.CoarseAccuracy
import OAI.Combinatorics.EditApproximation.Coarse.CoarseEstimator
import OAI.Combinatorics.EditApproximation.Coarse.CoarseSampling
import OAI.Combinatorics.EditApproximation.Coarse.CoarseProbability
import OAI.Combinatorics.EditApproximation.Coarse.CoarseTransforms
import OAI.Combinatorics.EditApproximation.Coarse.CoarseWork
import OAI.Combinatorics.EditApproximation.Coarse.CoarsePadding
import OAI.Combinatorics.EditApproximation.Coarse.CoarseInitial
import OAI.Combinatorics.EditApproximation.Coarse.CoarseSeed
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonAccounting
import OAI.Combinatorics.EditApproximation.Probability.Concentration
import OAI.Combinatorics.EditApproximation.Geometry.Cones
import OAI.Combinatorics.EditApproximation.Geometry.ConeLocality
import OAI.Combinatorics.EditApproximation.Geometry.Connections
import OAI.Combinatorics.EditApproximation.Geometry.Curvature
import OAI.Combinatorics.EditApproximation.Geometry.DomainCounts
import OAI.Combinatorics.EditApproximation.Geometry.DomainExponential
import OAI.Combinatorics.EditApproximation.Probability.Exact
import OAI.Combinatorics.EditApproximation.Probability.ExactSampling
import OAI.Combinatorics.EditApproximation.Probability.ExpectedRegret
import OAI.Combinatorics.EditApproximation.Geometry.FirstCrossing
import OAI.Combinatorics.EditApproximation.Probability.FiniteAssignments
import OAI.Combinatorics.EditApproximation.Geometry.GroupSampling
import OAI.Combinatorics.EditApproximation.Geometry.Grid
import OAI.Combinatorics.EditApproximation.Geometry.Leaves
import OAI.Combinatorics.EditApproximation.Geometry.LocalGrid
import OAI.Combinatorics.EditApproximation.Geometry.LocalInitialCones
import OAI.Combinatorics.EditApproximation.Geometry.InitialCones
import OAI.Combinatorics.EditApproximation.Geometry.InitialConeGrid
import OAI.Combinatorics.EditApproximation.Geometry.InitialConeTable
import OAI.Combinatorics.EditApproximation.Probability.Median
import OAI.Combinatorics.EditApproximation.Numerics.Numerics
import OAI.Combinatorics.EditApproximation.Numerics.NumericalWork
import OAI.Combinatorics.EditApproximation.Geometry.NodeRegret
import OAI.Combinatorics.EditApproximation.Geometry.ParameterSlack
import OAI.Combinatorics.EditApproximation.Geometry.Parameters
import OAI.Combinatorics.EditApproximation.Geometry.PartitionIntervals
import OAI.Combinatorics.EditApproximation.Numerics.RationalRefinement
import OAI.Combinatorics.EditApproximation.Probability.SampledRegret
import OAI.Combinatorics.EditApproximation.Geometry.StateGeometry
import OAI.Combinatorics.EditApproximation.Probability.ThresholdMoments
import OAI.Combinatorics.EditApproximation.Geometry.TreeAccounting
import OAI.Combinatorics.EditApproximation.Geometry.TreeParameters
import OAI.Combinatorics.EditApproximation.Geometry.Work
import OAI.Combinatorics.EditApproximation.Geometry.WeightedTreeWork
import OAI.Combinatorics.EditApproximation.Geometry.WideActions
import OAI.Combinatorics.EditApproximation.Geometry.BandGroupSampling
import OAI.Combinatorics.EditApproximation.Geometry.CellGroupSelection
import OAI.Combinatorics.EditApproximation.Geometry.ComparisonLiftBounds
import OAI.Combinatorics.EditApproximation.Refinement.ComputedGroupAccuracy
import OAI.Combinatorics.EditApproximation.Refinement.ComputedGroupNumerical
import OAI.Combinatorics.EditApproximation.Geometry.GroupCells
import OAI.Combinatorics.EditApproximation.Geometry.GroupNumerical
import OAI.Combinatorics.EditApproximation.Geometry.GroupSmallConstants
import OAI.Combinatorics.EditApproximation.Geometry.ListBandRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalGroupAccuracy
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalOnlineBand
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalNodeRegret
import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonEnergy
import OAI.Combinatorics.EditApproximation.Refinement.StageParameterBounds

import OAI.Combinatorics.EditApproximation.Geometry.ComparisonLiftStep
import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonCharges
import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonBad
import OAI.Combinatorics.EditApproximation.Geometry.BandDimension
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalUnskippedComparison
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalGenericRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalComparisonBand
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeGeneric
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeExpectation
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalExpectedRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalParentDraw
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementLocality
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalResampledRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalConditionalNode
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSelectionProgram
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSelectionResampling
import OAI.Combinatorics.EditApproximation.Probability.FiniteResampling
import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonPrediction
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeNear
import OAI.Combinatorics.EditApproximation.Geometry.UnskippedRegretBudget
import OAI.Combinatorics.EditApproximation.Refinement.ComputedStageParameters
import OAI.Combinatorics.EditApproximation.Refinement.ComputedStageTime
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalBoundsAllSeeds
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeBudget
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramLaw
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramRefreshWiring
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramNodeRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramComparisonRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramAccuracy
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalOnlineLocality
import OAI.Combinatorics.EditApproximation.Geometry.RefinementErrorTerms
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalDenominator
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalValueBits
import OAI.Combinatorics.EditApproximation.Numerics.RationalPruning
import OAI.Combinatorics.EditApproximation.Geometry.RefinementConeLocality
import OAI.Combinatorics.EditApproximation.Geometry.LocalCells
import OAI.Combinatorics.EditApproximation.Geometry.LocalRefinementCones
import OAI.Combinatorics.EditApproximation.Geometry.GroupSamplingWork
import OAI.Combinatorics.EditApproximation.Geometry.LocalGroupCones
import OAI.Combinatorics.EditApproximation.Geometry.RoundedGroupStates
import OAI.Combinatorics.EditApproximation.Geometry.DyadicQueryWindow
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtree
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeMass
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeCharges
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeExpectation
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeBad
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeGeneric
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreePrediction
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeNear
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeBudget
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramSubtreeRegret
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramStateAccuracy
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedMedian
import OAI.Combinatorics.EditApproximation.Geometry.ActualRoundedGroupInputs
import OAI.Combinatorics.EditApproximation.Geometry.SharedGroupInputBudget
import OAI.Combinatorics.EditApproximation.Geometry.SeedPassNumerics
import OAI.Combinatorics.EditApproximation.Geometry.SeedFactorSchedule
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalQueryBudget
import OAI.Combinatorics.EditApproximation.Geometry.LocalGroupBudget
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedPass
import OAI.Combinatorics.EditApproximation.Probability.AdaptiveSeedLaw
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedTables
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedSchedule
import OAI.Combinatorics.EditApproximation.Binary.BinaryMemo
import OAI.Combinatorics.EditApproximation.Geometry.CurrentQueryInputs
import OAI.Combinatorics.EditApproximation.Geometry.GroupInputDependence
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalGroupProgram
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalWarmup
import OAI.Combinatorics.EditApproximation.Probability.FiniteSeedFinal
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalCoarseSeedLaw
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalFinalAccuracy
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalConditionalAccuracy
import OAI.Combinatorics.EditApproximation.Geometry.LocalWideStep
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalRefinement
import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalRefinementEquality
import OAI.Combinatorics.EditApproximation.Refinement.ComputedCurrentQueryBudget

import OAI.Combinatorics.EditApproximation.AlmostLinear

/-!
# Almost-linear approximation of edit distance

A uniform binary randomized approximation scheme attains success probability
at least two thirds, returns zero on equal strings, uses almost-linear expected
work for each fixed binary accuracy, and has polynomial space on every outcome.
Finite Bernstein concentration discharges the hypotheses of its conditional
accuracy and work bounds.
-/