Details

sample277.0ms

Algorithm

intervals

Results

67.0ms	98×	body	160	valid
32.0ms	116×	body	320	valid
22.0ms	256×	body	80	nan
20.0ms	512×	pre	80	true
6.0ms	26×	body	80	valid
5.0ms	16×	body	640	valid

simplify137.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	128
5	128
4	119
3	86
2	46
1	25
0	14

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (- a) (* 4.0 c) (* b b)))
0.1b	(fma (- a) (* 4.0 c) (* b b))
0.1b	(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
26.0b	(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 110

Calls

4 calls:

2.0ms	(sqrt (fma (- a) (* 4.0 c) (* b b)))
1.0ms	(fma (- a) (* 4.0 c) (* b b))
44.0ms	(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
26.0ms	(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

series615.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt (fma (- a) (* 4.0 c) (* b b)))
112.0ms	(fma (- a) (* 4.0 c) (* b b))
202.0ms	(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
160.0ms	(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

simplify722.0ms

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1064
1	336
0	152

prune623.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 4.0 (* c (- a)) (* b b))
0.1b	(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
0.2b	(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
0.3b	(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `fma-udef` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

1.0ms	(fma 4.0 (* c (- a)) (* b b))
18.0ms	(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
43.0ms	(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
20.0ms	(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

series852.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma 4.0 (* c (- a)) (* b b))
114.0ms	(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
356.0ms	(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)
291.0ms	(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))

simplify1.3s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	2635
1	605
0	251

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2)))))
0.1b	(fma (* c a) (- 4.0) (pow b 2))
0.1b	(+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))
0.3b	(/ (* a (* (- 4.0) c)) (* a (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-cbrt-cube` `add-exp-log`
11×	`*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `associate-*r/` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-l` `flip-+`
2×	`associate-/r/` `distribute-lft-out`
1×	`distribute-lft-neg-out` `distribute-rgt-in` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `distribute-lft-in` `times-frac` `pow-prod-down` `distribute-frac-neg` `-commutative` `distribute-rgt-neg-out` `fma-udef` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

47.0ms	(* a (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2)))))
1.0ms	(fma (* c a) (- 4.0) (pow b 2))
11.0ms	(+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))
47.0ms	(/ (* a (* (- 4.0) c)) (* a (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* a (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2)))))
113.0ms	(fma (* c a) (- 4.0) (pow b 2))
127.0ms	(+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))
249.0ms	(/ (* a (* (- 4.0) c)) (* a (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))))

simplify1.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	3428
1	502
0	157

prune692.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* c a) (- 4.0) (pow b 2)))
0.1b	(/ (/ (- (* c 4.0)) (/ a a)) (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2)))))
0.1b	(fma (* c a) (- 4.0) (pow b 2))
0.1b	(+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

992×	`times-frac`
540×	`*-un-lft-identity`
371×	`add-sqr-sqrt`
370×	`add-cube-cbrt`
85×	`distribute-lft-out`
83×	`associate-/l*`
65×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
36×	`div-inv`
13×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r/`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`flip3-+` `div-sub` `distribute-frac-neg` `flip-+`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 484

Calls

4 calls:

2.0ms	(sqrt (fma (* c a) (- 4.0) (pow b 2)))
48.0ms	(/ (/ (- (* c 4.0)) (/ a a)) (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2)))))
0.0ms	(fma (* c a) (- 4.0) (pow b 2))
6.0ms	(+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (fma (* c a) (- 4.0) (pow b 2)))
258.0ms	(/ (/ (- (* c 4.0)) (/ a a)) (+ b (sqrt (fma (* c a) (- 4.0) (pow b 2)))))
88.0ms	(fma (* c a) (- 4.0) (pow b 2))
127.0ms	(+ b (sqrt (fma (* c a) (- 4.0) (pow b 2))))

simplify1.4s

Counts

496 → 496

Iterations

Iter	Nodes
done	5000
1	2413
0	858

prune2.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes215.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.5m

Iterations

Iter	Nodes
done	5001
414	4989
413	4977
412	4965
411	4953
410	4941
409	4929
408	4917
407	4905
406	4893
405	4881
404	4869
403	4857
402	4845
401	4833
400	4821
399	4809
398	4797
397	4785
396	4773
395	4761
394	4749
393	4737
392	4725
391	4713
390	4701
389	4689
388	4677
387	4665
386	4653
385	4641
384	4629
383	4617
382	4605
381	4593
380	4581
379	4569
378	4557
377	4545
376	4533
375	4521
374	4509
373	4497
372	4485
371	4473
370	4461
369	4449
368	4437
367	4425
366	4413
365	4401
364	4389
363	4377
362	4365
361	4353
360	4341
359	4329
358	4317
357	4305
356	4293
355	4281
354	4269
353	4257
352	4245
351	4233
350	4221
349	4209
348	4197
347	4185
346	4173
345	4161
344	4149
343	4137
342	4125
341	4113
340	4101
339	4089
338	4077
337	4065
336	4053
335	4041
334	4029
333	4017
332	4005
331	3993
330	3981
329	3969
328	3957
327	3945
326	3933
325	3921
324	3909
323	3897
322	3885
321	3873
320	3861
319	3849
318	3837
317	3825
316	3813
315	3801
314	3789
313	3777
312	3765
311	3753
310	3741
309	3729
308	3717
307	3705
306	3693
305	3681
304	3669
303	3657
302	3645
301	3633
300	3621
299	3609
298	3597
297	3585
296	3573
295	3561
294	3549
293	3537
292	3525
291	3513
290	3501
289	3489
288	3477
287	3465
286	3453
285	3441
284	3429
283	3417
282	3405
281	3393
280	3381
279	3369
278	3357
277	3345
276	3333
275	3321
274	3309
273	3297
272	3285
271	3273
270	3261
269	3249
268	3237
267	3225
266	3213
265	3201
264	3189
263	3177
262	3165
261	3153
260	3141
259	3129
258	3117
257	3105
256	3093
255	3081
254	3069
253	3057
252	3045
251	3033
250	3021
249	3009
248	2997
247	2985
246	2973
245	2961
244	2949
243	2937
242	2925
241	2913
240	2901
239	2889
238	2877
237	2865
236	2853
235	2841
234	2829
233	2817
232	2805
231	2793
230	2781
229	2769
228	2757
227	2745
226	2733
225	2721
224	2709
223	2697
222	2685
221	2673
220	2661
219	2649
218	2637
217	2625
216	2613
215	2601
214	2589
213	2577
212	2565
211	2553
210	2541
209	2529
208	2517
207	2505
206	2493
205	2481
204	2469
203	2457
202	2445
201	2433
200	2421
199	2409
198	2397
197	2385
196	2373
195	2361
194	2349
193	2337
192	2325
191	2313
190	2301
189	2289
188	2277
187	2265
186	2253
185	2241
184	2229
183	2217
182	2205
181	2193
180	2181
179	2169
178	2157
177	2145
176	2133
175	2121
174	2109
173	2097
172	2085
171	2073
170	2061
169	2049
168	2037
167	2025
166	2013
165	2001
164	1989
163	1977
162	1965
161	1953
160	1941
159	1929
158	1917
157	1905
156	1893
155	1881
154	1869
153	1857
152	1845
151	1833
150	1821
149	1809
148	1797
147	1785
146	1773
145	1761
144	1749
143	1737
142	1725
141	1713
140	1701
139	1689
138	1677
137	1665
136	1653
135	1641
134	1629
133	1617
132	1605
131	1593
130	1581
129	1569
128	1557
127	1545
126	1533
125	1521
124	1509
123	1497
122	1485
121	1473
120	1461
119	1449
118	1437
117	1425
116	1413
115	1401
114	1389
113	1377
112	1365
111	1353
110	1341
109	1329
108	1317
107	1305
106	1293
105	1281
104	1269
103	1257
102	1245
101	1233
100	1221
99	1209
98	1197
97	1185
96	1173
95	1161
94	1149
93	1137
92	1125
91	1113
90	1101
89	1089
88	1077
87	1065
86	1053
85	1041
84	1029
83	1017
82	1005
81	993
80	981
79	969
78	957
77	945
76	933
75	921
74	909
73	897
72	885
71	873
70	861
69	849
68	837
67	825
66	813
65	801
64	789
63	777
62	765
61	753
60	741
59	729
58	717
57	705
56	693
55	681
54	669
53	657
52	645
51	633
50	621
49	609
48	597
47	585
46	573
45	561
44	549
43	537
42	525
41	513
40	501
39	489
38	477
37	465
36	453
35	441
34	429
33	417
32	405
31	393
30	381
29	369
28	357
27	345
26	333
25	321
24	309
23	297
22	285
21	273
20	261
19	249
18	237
17	225
16	213
15	201
14	189
13	177
12	165
11	153
10	141
9	129
8	117
7	105
6	93
5	81
4	69
3	55
2	37
1	26
0	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

806.0ms	8098×	body	80	nan
635.0ms	3577×	body	320	valid
460.0ms	16098×	pre	80	true
267.0ms	3042×	body	160	valid
110.0ms	467×	body	640	valid
43.0ms	914×	body	80	valid