Variance-aware gradient reduction trees / results.json
Failed on benchmark
1{
2 "identity_check": {
3 "tree": "balanced_8",
4 "Lambda1": 24.0,
5 "Lambda2": 112.0,
6 "rows": [
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28 {
29 "mu": 0.25,
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34 },
35 {
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54 "relative_error": 4.613461460484568e-05
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61 "relative_error": 8.114713936975196e-05
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70 {
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75 "relative_error": 2.9639161850825672e-05
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77 {
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84 {
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87 "predicted": 1062.0,
88 "observed": 1060.8498380366138,
89 "relative_error": 0.0010830150314370562
90 }
91 ],
92 "max_relative_error": 0.0065925974467937465
93 },
94 "roundoff_scaling": {
95 "rows": [
96 {
97 "u": 0.03125,
98 "observed_mse": 0.015840501337322743,
99 "predicted_mse": 0.015900059237790126,
100 "ratio_obs_over_u2": 16.22067336941849,
101 "relative_error": 0.003745765948206658
102 },
103 {
104 "u": 0.0078125,
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107 "ratio_obs_over_u2": 16.101927003562103,
108 "relative_error": 0.011039024807960639
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110 {
111 "u": 0.001953125,
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114 "ratio_obs_over_u2": 16.11741179988249,
115 "relative_error": 0.010087967256509088
116 },
117 {
118 "u": 0.00048828125,
119 "observed_mse": 3.8823653113995034e-06,
120 "predicted_mse": 3.881850399851105e-06,
121 "ratio_obs_over_u2": 16.283820355064183,
122 "relative_error": 0.00013264590217550311
123 }
124 ],
125 "loglog_slope": 1.999089838367662,
126 "predicted_slope": 2.0
127 },
128 "variance_topology_sweep": [
129 {
130 "ratio": 1,
131 "balanced_cost": 24.0,
132 "huffman_cost": 24.0,
133 "predicted_gain_fraction": 0.0,
134 "huffman_depth_high_variance": 3
135 },
136 {
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139 "huffman_cost": 27.0,
140 "predicted_gain_fraction": 0.0,
141 "huffman_depth_high_variance": 3
142 },
143 {
144 "ratio": 4,
145 "balanced_cost": 33.0,
146 "huffman_cost": 31.0,
147 "predicted_gain_fraction": 0.06060606060606055,
148 "huffman_depth_high_variance": 2
149 },
150 {
151 "ratio": 8,
152 "balanced_cost": 45.0,
153 "huffman_cost": 35.0,
154 "predicted_gain_fraction": 0.2222222222222222,
155 "huffman_depth_high_variance": 1
156 },
157 {
158 "ratio": 16,
159 "balanced_cost": 69.0,
160 "huffman_cost": 43.0,
161 "predicted_gain_fraction": 0.37681159420289856,
162 "huffman_depth_high_variance": 1
163 },
164 {
165 "ratio": 32,
166 "balanced_cost": 117.0,
167 "huffman_cost": 59.0,
168 "predicted_gain_fraction": 0.49572649572649574,
169 "huffman_depth_high_variance": 1
170 },
171 {
172 "ratio": 64,
173 "balanced_cost": 213.0,
174 "huffman_cost": 91.0,
175 "predicted_gain_fraction": 0.5727699530516432,
176 "huffman_depth_high_variance": 1
177 }
178 ],
179 "heterogeneous_monte_carlo": [
180 {
181 "tree": "balanced",
182 "predicted_cost": 69.0,
183 "observed_cost": 68.61639584778041,
184 "relative_error": 0.005559480466950578,
185 "depths": {
186 "0": 3,
187 "1": 3,
188 "2": 3,
189 "3": 3,
190 "4": 3,
191 "5": 3,
192 "6": 3,
193 "7": 3
194 }
195 },
196 {
197 "tree": "huffman",
198 "predicted_cost": 43.0,
199 "observed_cost": 42.8624064748514,
200 "relative_error": 0.0031998494220605274,
201 "depths": {
202 "7": 3,
203 "1": 4,
204 "2": 4,
205 "3": 4,
206 "4": 4,
207 "5": 4,
208 "6": 4,
209 "0": 1
210 }
211 }
212 ],
213 "notes": [
214 "All costs omit common nu*u^2 factors. Huffman minimizes sum sigma_i^2 depth_i among binary trees.",
215 "The roundoff simulation uses the stated conditional Gaussian local-noise approximation."
216 ]
217}