1{
  2  "seed": 1303,
  3  "singular_decay": [
  4    {
  5      "h": 4,
  6      "singular_values": [
  7        1.0000000000000002,
  8        0.032471995935982094,
  9        0.0007112239242100824,
 10        1.0485620007805735e-05
 11      ],
 12      "geometric_bound_check": [
 13        {
 14          "N": 0,
 15          "observed": 1.0000000000000002,
 16          "predicted_bound": 1.0,
 17          "satisfies": true
 18        },
 19        {
 20          "N": 1,
 21          "observed": 0.032471995935982094,
 22          "predicted_bound": 0.25,
 23          "satisfies": true
 24        },
 25        {
 26          "N": 2,
 27          "observed": 0.0007112239242100824,
 28          "predicted_bound": 0.0625,
 29          "satisfies": true
 30        },
 31        {
 32          "N": 3,
 33          "observed": 1.0485620007805735e-05,
 34          "predicted_bound": 0.015625,
 35          "satisfies": true
 36        }
 37      ],
 38      "ratios": [
 39        0.03247199593598209,
 40        0.021902685797702316,
 41        0.01474306424583726
 42      ]
 43    },
 44    {
 45      "h": 8,
 46      "singular_values": [
 47        1.0000000000000002,
 48        0.037517497868420686,
 49        0.001079614010971153,
 50        2.7861455019730973e-05,
 51        6.383014383184403e-07,
 52        1.250699384949905e-08
 53      ],
 54      "geometric_bound_check": [
 55        {
 56          "N": 0,
 57          "observed": 1.0000000000000002,
 58          "predicted_bound": 1.0,
 59          "satisfies": true
 60        },
 61        {
 62          "N": 1,
 63          "observed": 0.037517497868420686,
 64          "predicted_bound": 0.25,
 65          "satisfies": true
 66        },
 67        {
 68          "N": 2,
 69          "observed": 0.001079614010971153,
 70          "predicted_bound": 0.0625,
 71          "satisfies": true
 72        },
 73        {
 74          "N": 3,
 75          "observed": 2.7861455019730973e-05,
 76          "predicted_bound": 0.015625,
 77          "satisfies": true
 78        },
 79        {
 80          "N": 4,
 81          "observed": 6.383014383184403e-07,
 82          "predicted_bound": 0.00390625,
 83          "satisfies": true
 84        }
 85      ],
 86      "ratios": [
 87        0.03751749786842068,
 88        0.02877627966442528,
 89        0.02580686684000012,
 90        0.022909838623517934
 91      ]
 92    },
 93    {
 94      "h": 16,
 95      "singular_values": [
 96        1.0,
 97        0.040042040676386906,
 98        0.001269155576889523,
 99        3.8086545883880336e-05,
100        1.1003527416435871e-06,
101        3.057672838400633e-08
102      ],
103      "geometric_bound_check": [
104        {
105          "N": 0,
106          "observed": 1.0,
107          "predicted_bound": 1.0,
108          "satisfies": true
109        },
110        {
111          "N": 1,
112          "observed": 0.040042040676386906,
113          "predicted_bound": 0.25,
114          "satisfies": true
115        },
116        {
117          "N": 2,
118          "observed": 0.001269155576889523,
119          "predicted_bound": 0.0625,
120          "satisfies": true
121        },
122        {
123          "N": 3,
124          "observed": 3.8086545883880336e-05,
125          "predicted_bound": 0.015625,
126          "satisfies": true
127        },
128        {
129          "N": 4,
130          "observed": 1.1003527416435871e-06,
131          "predicted_bound": 0.00390625,
132          "satisfies": true
133        }
134      ],
135      "ratios": [
136        0.040042040676386906,
137        0.03169557683502264,
138        0.030009359433477618,
139        0.028890851509569368
140      ]
141    },
142    {
143      "h": 32,
144      "singular_values": [
145        0.9999999999999999,
146        0.04128677317325391,
147        0.0013602423417570098,
148        4.3008279618050345e-05,
149        1.3344305065041076e-06,
150        4.0828908628957114e-08
151      ],
152      "geometric_bound_check": [
153        {
154          "N": 0,
155          "observed": 0.9999999999999999,
156          "predicted_bound": 1.0,
157          "satisfies": true
158        },
159        {
160          "N": 1,
161          "observed": 0.04128677317325391,
162          "predicted_bound": 0.25,
163          "satisfies": true
164        },
165        {
166          "N": 2,
167          "observed": 0.0013602423417570098,
168          "predicted_bound": 0.0625,
169          "satisfies": true
170        },
171        {
172          "N": 3,
173          "observed": 4.3008279618050345e-05,
174          "predicted_bound": 0.015625,
175          "satisfies": true
176        },
177        {
178          "N": 4,
179          "observed": 1.3344305065041076e-06,
180          "predicted_bound": 0.00390625,
181          "satisfies": true
182        }
183      ],
184      "ratios": [
185        0.04128677317325392,
186        0.032946201342714566,
187        0.03161810090582611,
188        0.03102729331084553
189      ]
190    },
191    {
192      "h": 64,
193      "singular_values": [
194        0.9999999999999999,
195        0.04190170645943303,
196        0.0014039556258478786,
197        4.529941550762505e-05,
198        1.4412151135005145e-06,
199        4.549727726114446e-08
200      ],
201      "geometric_bound_check": [
202        {
203          "N": 0,
204          "observed": 0.9999999999999999,
205          "predicted_bound": 1.0,
206          "satisfies": true
207        },
208        {
209          "N": 1,
210          "observed": 0.04190170645943303,
211          "predicted_bound": 0.25,
212          "satisfies": true
213        },
214        {
215          "N": 2,
216          "observed": 0.0014039556258478786,
217          "predicted_bound": 0.0625,
218          "satisfies": true
219        },
220        {
221          "N": 3,
222          "observed": 4.529941550762505e-05,
223          "predicted_bound": 0.015625,
224          "satisfies": true
225        },
226        {
227          "N": 4,
228          "observed": 1.4412151135005145e-06,
229          "predicted_bound": 0.00390625,
230          "satisfies": true
231        }
232      ],
233      "ratios": [
234        0.04190170645943304,
235        0.0335059295784794,
236        0.03226556072971877,
237        0.031815313671275096
238      ]
239    }
240  ],
241  "rank_scaling": [
242    {
243      "h": 8,
244      "epsilon": 0.01,
245      "observed_rank": 2,
246      "predicted_rank_bound": 4,
247      "bound_holds": true
248    },
249    {
250      "h": 8,
251      "epsilon": 0.001,
252      "observed_rank": 3,
253      "predicted_rank_bound": 5,
254      "bound_holds": true
255    },
256    {
257      "h": 8,
258      "epsilon": 0.0001,
259      "observed_rank": 3,
260      "predicted_rank_bound": 7,
261      "bound_holds": true
262    },
263    {
264      "h": 16,
265      "epsilon": 0.01,
266      "observed_rank": 2,
267      "predicted_rank_bound": 4,
268      "bound_holds": true
269    },
270    {
271      "h": 16,
272      "epsilon": 0.001,
273      "observed_rank": 3,
274      "predicted_rank_bound": 5,
275      "bound_holds": true
276    },
277    {
278      "h": 16,
279      "epsilon": 0.0001,
280      "observed_rank": 3,
281      "predicted_rank_bound": 7,
282      "bound_holds": true
283    },
284    {
285      "h": 32,
286      "epsilon": 0.01,
287      "observed_rank": 2,
288      "predicted_rank_bound": 4,
289      "bound_holds": true
290    },
291    {
292      "h": 32,
293      "epsilon": 0.001,
294      "observed_rank": 3,
295      "predicted_rank_bound": 5,
296      "bound_holds": true
297    },
298    {
299      "h": 32,
300      "epsilon": 0.0001,
301      "observed_rank": 3,
302      "predicted_rank_bound": 7,
303      "bound_holds": true
304    },
305    {
306      "h": 64,
307      "epsilon": 0.01,
308      "observed_rank": 2,
309      "predicted_rank_bound": 4,
310      "bound_holds": true
311    },
312    {
313      "h": 64,
314      "epsilon": 0.001,
315      "observed_rank": 3,
316      "predicted_rank_bound": 5,
317      "bound_holds": true
318    },
319    {
320      "h": 64,
321      "epsilon": 0.0001,
322      "observed_rank": 3,
323      "predicted_rank_bound": 7,
324      "bound_holds": true
325    }
326  ],
327  "application_scaling": [
328    {
329      "h": 64,
330      "n_left": 256,
331      "n_right": 64,
332      "rank": 4,
333      "relative_output_error": 1.8506525884115408e-06,
334      "dense_ms": 0.07653875013602374,
335      "factorized_ms": 0.03605612505452882,
336      "measured_speedup": 2.1227669368317246,
337      "ideal_work_ratio": 12.8
338    },
339    {
340      "h": 128,
341      "n_left": 512,
342      "n_right": 128,
343      "rank": 4,
344      "relative_output_error": 1.5201875517994328e-06,
345      "dense_ms": 0.09929849989021022,
346      "factorized_ms": 0.04479525000533613,
347      "measured_speedup": 2.2167194039185296,
348      "ideal_work_ratio": 25.6
349    },
350    {
351      "h": 256,
352      "n_left": 1024,
353      "n_right": 256,
354      "rank": 4,
355      "relative_output_error": 1.6068503168438619e-06,
356      "dense_ms": 0.5982622499232093,
357      "factorized_ms": 0.08230074990933645,
358      "measured_speedup": 7.269219910903153,
359      "ideal_work_ratio": 51.2
360    },
361    {
362      "h": 512,
363      "n_left": 2048,
364      "n_right": 512,
365      "rank": 4,
366      "relative_output_error": 9.895432789404913e-07,
367      "dense_ms": 1.5680517503824376,
368      "factorized_ms": 0.1368737498523842,
369      "measured_speedup": 11.456190482642231,
370      "ideal_work_ratio": 102.4
371    }
372  ]
373}