Details

sample147.0ms

Algorithm

intervals

Results

27.0ms	151×	body	160	valid
24.0ms	515×	pre	80	true
24.0ms	259×	body	80	nan
14.0ms	49×	body	320	valid
5.0ms	56×	body	80	valid

simplify132.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4 a) c)))
0.1b	(- (* b b) (* (* 4 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
35.7b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

9.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(- (* b b) (* (* 4 a) c))
57.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
50.0ms	(- (* b b) (* (* 4 a) c))
120.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))

simplify1.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1454
1	435
0	166

prune514.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.4b

localize5.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune61.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(/ (* -2 (/ (* a c) b)) (* 2 a))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 57

Calls

2 calls:

12.0ms	(/ (* a c) b)
30.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))

series43.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(/ (* a c) b)
22.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify1.5s

Counts

63 → 63

Iterations

Iter	Nodes
done	5011
2	2170
1	346
0	113

prune378.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 5.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (/ (* a c) b))
0.3b	(/ (* a c) b)
0.3b	(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
0.4b	(expm1 (log1p (/ (* a c) b)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
5×	`expm1-log1p-u` `prod-exp` `cbrt-unprod`
4×	`pow1` `associate-/r*` `times-frac` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 72

Calls

4 calls:

0.0ms	(log1p (/ (* a c) b))
10.0ms	(/ (* a c) b)
18.0ms	(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
0.0ms	(expm1 (log1p (/ (* a c) b)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(log1p (/ (* a c) b))
35.0ms	(/ (* a c) b)
125.0ms	(/ (* -2 (expm1 (log1p (/ (* a c) b)))) (* 2 a))
123.0ms	(expm1 (log1p (/ (* a c) b)))

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5005
2	1781
1	364
0	146

prune381.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.3b

regimes786.0ms

Accuracy

24% (5.2b remaining)

Error of 10.4b against oracle of 5.2b and baseline of 12.0b

bsearch6.0ms

simplify1.6s

Iterations

Iter	Nodes
done	5001
551	4993
550	4983
549	4975
548	4965
547	4957
546	4947
545	4939
544	4929
543	4921
542	4911
541	4903
540	4893
539	4885
538	4875
537	4867
536	4857
535	4849
534	4839
533	4831
532	4821
531	4813
530	4803
529	4795
528	4785
527	4777
526	4767
525	4759
524	4749
523	4741
522	4731
521	4723
520	4713
519	4705
518	4695
517	4687
516	4677
515	4669
514	4659
513	4651
512	4641
511	4633
510	4623
509	4615
508	4605
507	4597
506	4587
505	4579
504	4569
503	4561
502	4551
501	4543
500	4533
499	4525
498	4515
497	4507
496	4497
495	4489
494	4479
493	4471
492	4461
491	4453
490	4443
489	4435
488	4425
487	4417
486	4407
485	4399
484	4389
483	4381
482	4371
481	4363
480	4353
479	4345
478	4335
477	4327
476	4317
475	4309
474	4299
473	4291
472	4281
471	4273
470	4263
469	4255
468	4245
467	4237
466	4227
465	4219
464	4209
463	4201
462	4191
461	4183
460	4173
459	4165
458	4155
457	4147
456	4137
455	4129
454	4119
453	4111
452	4101
451	4093
450	4083
449	4075
448	4065
447	4057
446	4047
445	4039
444	4029
443	4021
442	4011
441	4003
440	3993
439	3985
438	3975
437	3967
436	3957
435	3949
434	3939
433	3931
432	3921
431	3913
430	3903
429	3895
428	3885
427	3877
426	3867
425	3859
424	3849
423	3841
422	3831
421	3823
420	3813
419	3805
418	3795
417	3787
416	3777
415	3769
414	3759
413	3751
412	3741
411	3733
410	3723
409	3715
408	3705
407	3697
406	3687
405	3679
404	3669
403	3661
402	3651
401	3643
400	3633
399	3625
398	3615
397	3607
396	3597
395	3589
394	3579
393	3571
392	3561
391	3553
390	3543
389	3535
388	3525
387	3517
386	3507
385	3499
384	3489
383	3481
382	3471
381	3463
380	3453
379	3445
378	3435
377	3427
376	3417
375	3409
374	3399
373	3391
372	3381
371	3373
370	3363
369	3355
368	3345
367	3337
366	3327
365	3319
364	3309
363	3301
362	3291
361	3283
360	3273
359	3265
358	3255
357	3247
356	3237
355	3229
354	3219
353	3211
352	3201
351	3193
350	3183
349	3175
348	3165
347	3157
346	3147
345	3139
344	3129
343	3121
342	3111
341	3103
340	3093
339	3085
338	3075
337	3067
336	3057
335	3049
334	3039
333	3031
332	3021
331	3013
330	3003
329	2995
328	2985
327	2977
326	2967
325	2959
324	2949
323	2941
322	2931
321	2923
320	2913
319	2905
318	2895
317	2887
316	2877
315	2869
314	2859
313	2851
312	2841
311	2833
310	2823
309	2815
308	2805
307	2797
306	2787
305	2779
304	2769
303	2761
302	2751
301	2743
300	2733
299	2725
298	2715
297	2707
296	2697
295	2689
294	2679
293	2671
292	2661
291	2653
290	2643
289	2635
288	2625
287	2617
286	2607
285	2599
284	2589
283	2581
282	2571
281	2563
280	2553
279	2545
278	2535
277	2527
276	2517
275	2509
274	2499
273	2491
272	2481
271	2473
270	2463
269	2455
268	2445
267	2437
266	2427
265	2419
264	2409
263	2401
262	2391
261	2383
260	2373
259	2365
258	2355
257	2347
256	2337
255	2329
254	2319
253	2311
252	2301
251	2293
250	2283
249	2275
248	2265
247	2257
246	2247
245	2239
244	2229
243	2221
242	2211
241	2203
240	2193
239	2185
238	2175
237	2167
236	2157
235	2149
234	2139
233	2131
232	2121
231	2113
230	2103
229	2095
228	2085
227	2077
226	2067
225	2059
224	2049
223	2041
222	2031
221	2023
220	2013
219	2005
218	1995
217	1987
216	1977
215	1969
214	1959
213	1951
212	1941
211	1933
210	1923
209	1915
208	1905
207	1897
206	1887
205	1879
204	1869
203	1861
202	1851
201	1843
200	1833
199	1825
198	1815
197	1807
196	1797
195	1789
194	1779
193	1771
192	1761
191	1753
190	1743
189	1735
188	1725
187	1717
186	1707
185	1699
184	1689
183	1681
182	1671
181	1663
180	1653
179	1645
178	1635
177	1627
176	1617
175	1609
174	1599
173	1591
172	1581
171	1573
170	1563
169	1555
168	1545
167	1537
166	1527
165	1519
164	1509
163	1501
162	1491
161	1483
160	1473
159	1465
158	1455
157	1447
156	1437
155	1429
154	1419
153	1411
152	1401
151	1393
150	1383
149	1375
148	1365
147	1357
146	1347
145	1339
144	1329
143	1321
142	1311
141	1303
140	1293
139	1285
138	1275
137	1267
136	1257
135	1249
134	1239
133	1231
132	1221
131	1213
130	1203
129	1195
128	1185
127	1177
126	1167
125	1159
124	1149
123	1141
122	1131
121	1123
120	1113
119	1105
118	1095
117	1087
116	1077
115	1069
114	1059
113	1051
112	1041
111	1033
110	1023
109	1015
108	1005
107	997
106	987
105	979
104	969
103	961
102	951
101	943
100	933
99	925
98	915
97	907
96	897
95	889
94	879
93	871
92	861
91	853
90	843
89	835
88	825
87	817
86	807
85	799
84	789
83	781
82	771
81	763
80	753
79	745
78	735
77	727
76	717
75	709
74	699
73	691
72	681
71	673
70	663
69	655
68	645
67	637
66	627
65	619
64	609
63	601
62	591
61	583
60	573
59	565
58	555
57	547
56	537
55	529
54	519
53	511
52	501
51	493
50	483
49	475
48	465
47	457
46	447
45	439
44	429
43	421
42	411
41	403
40	393
39	385
38	375
37	367
36	357
35	349
34	339
33	331
32	321
31	313
30	303
29	295
28	285
27	277
26	267
25	259
24	249
23	241
22	231
21	223
20	213
19	205
18	195
17	187
16	177
15	169
14	159
13	151
12	141
11	133
10	123
9	115
8	105
7	97
6	87
5	79
4	65
3	55
2	40
1	36
0	25

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	4837×	body	160	valid
1.2s	8353×	body	80	nan
897.0ms	16353×	pre	80	true
426.0ms	1380×	body	320	valid
147.0ms	1783×	body	80	valid