Details

sample240.0ms

Algorithm

intervals

Results

75.0ms	40×	body	2560	valid
12.0ms	183×	body	80	valid
11.0ms	35×	body	1280	valid
9.0ms	79×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify131.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

113.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
28.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
39.0ms	(- (* b_2 b_2) (* a c))
136.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
133.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1655
1	405
0	164

prune803.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize34.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
3.5b	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
7.7b	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
24.2b	(sqrt (fma a (- c) (* b_2 b_2)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
228×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
45×	`associate-/l*`
33×	`distribute-lft-out`
16×	`neg-mul-1`
15×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/` `distribute-neg-frac`
7×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

4 → 289

Calls

4 calls:

13.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
98.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
66.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
3.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
216.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
277.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
149.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

simplify650.0ms

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	1066
0	420

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
1.6b	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
11.6b	(/ (* c a) a)
24.2b	(sqrt (fma a (- c) (pow b_2 2)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
44×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-lft-out`
8×	`associate-/l*`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`clear-num` `frac-2neg` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

35.0ms	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
11.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
15.0ms	(/ (* c a) a)
3.0ms	(sqrt (fma a (- c) (pow b_2 2)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
93.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
10.0ms	(/ (* c a) a)
106.0ms	(sqrt (fma a (- c) (pow b_2 2)))

simplify1.3s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	2395
1	472
0	185

prune817.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a (- c) (* b_2 b_2))
0.1b	(/ (/ c 1) (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
1.6b	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
24.2b	(sqrt (fma a (- c) (* b_2 b_2)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
85×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
15×	`distribute-lft-out`
13×	`associate-/l*`
11×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `sqrt-prod`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `fma-udef` `associate-/l/`

Counts

4 → 131

Calls

4 calls:

0.0ms	(fma a (- c) (* b_2 b_2))
30.0ms	(/ (/ c 1) (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
11.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
3.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma a (- c) (* b_2 b_2))
241.0ms	(/ (/ c 1) (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
100.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
90.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

simplify1.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	2548
1	532
0	213

prune632.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes359.0ms

bsearch226.0ms

Steps

Iters	Range	Point
9	2.1340360609407003e+79	6.102484722804822e+84	1.0166171304055961e+83
6	-9.106238092000907e-243	-2.101224228167501e-243	-2.1209008810311313e-243
8	-7.706925888451307e+24	-4.0529501114613944e+21	-7.604193036648139e+24

Iters

Range

Point

2.1340360609407003e+79

6.102484722804822e+84

1.0166171304055961e+83

-9.106238092000907e-243

-2.101224228167501e-243

-2.1209008810311313e-243

-7.706925888451307e+24

-4.0529501114613944e+21

-7.604193036648139e+24

simplify9.8m

Iterations

Iter	Nodes
674	2740
673	2736
672	2732
671	2728
670	2724
669	2720
668	2716
667	2712
666	2708
665	2704
664	2700
663	2696
662	2692
661	2688
660	2684
659	2680
658	2676
657	2672
656	2668
655	2664
654	2660
653	2656
652	2652
651	2648
650	2644
649	2640
648	2636
647	2632
646	2628
645	2624
644	2620
643	2616
642	2612
641	2608
640	2604
639	2600
638	2596
637	2592
636	2588
635	2584
634	2580
633	2576
632	2572
631	2568
630	2564
629	2560
628	2556
627	2552
626	2548
625	2544
624	2540
623	2536
622	2532
621	2528
620	2524
619	2520
618	2516
617	2512
616	2508
615	2504
614	2500
613	2496
612	2492
611	2488
610	2484
609	2480
608	2476
607	2472
606	2468
605	2464
604	2460
603	2456
602	2452
601	2448
600	2444
599	2440
598	2436
597	2432
596	2428
595	2424
594	2420
593	2416
592	2412
591	2408
590	2404
589	2400
588	2396
587	2392
586	2388
585	2384
584	2380
583	2376
582	2372
581	2368
580	2364
579	2360
578	2356
577	2352
576	2348
575	2344
574	2340
573	2336
572	2332
571	2328
570	2324
569	2320
568	2316
567	2312
566	2308
565	2304
564	2300
563	2296
562	2292
561	2288
560	2284
559	2280
558	2276
557	2272
556	2268
555	2264
554	2260
553	2256
552	2252
551	2248
550	2244
549	2240
548	2236
547	2232
546	2228
545	2224
544	2220
543	2216
542	2212
541	2208
540	2204
539	2200
538	2196
537	2192
536	2188
535	2184
534	2180
533	2176
532	2172
531	2168
530	2164
529	2160
528	2156
527	2152
526	2148
525	2144
524	2140
523	2136
522	2132
521	2128
520	2124
519	2120
518	2116
517	2112
516	2108
515	2104
514	2100
513	2096
512	2092
511	2088
510	2084
509	2080
508	2076
507	2072
506	2068
505	2064
504	2060
503	2056
502	2052
501	2048
500	2044
499	2040
498	2036
497	2032
496	2028
495	2024
494	2020
493	2016
492	2012
491	2008
490	2004
489	2000
488	1996
487	1992
486	1988
485	1984
484	1980
483	1976
482	1972
481	1968
480	1964
479	1960
478	1956
477	1952
476	1948
475	1944
474	1940
473	1936
472	1932
471	1928
470	1924
469	1920
468	1916
467	1912
466	1908
465	1904
464	1900
463	1896
462	1892
461	1888
460	1884
459	1880
458	1876
457	1872
456	1868
455	1864
454	1860
453	1856
452	1852
451	1848
450	1844
449	1840
448	1836
447	1832
446	1828
445	1824
444	1820
443	1816
442	1812
441	1808
440	1804
439	1800
438	1796
437	1792
436	1788
435	1784
434	1780
433	1776
432	1772
431	1768
430	1764
429	1760
428	1756
427	1752
426	1748
425	1744
424	1740
423	1736
422	1732
421	1728
420	1724
419	1720
418	1716
417	1712
416	1708
415	1704
414	1700
413	1696
412	1692
411	1688
410	1684
409	1680
408	1676
407	1672
406	1668
405	1664
404	1660
403	1656
402	1652
401	1648
400	1644
399	1640
398	1636
397	1632
396	1628
395	1624
394	1620
393	1616
392	1612
391	1608
390	1604
389	1600
388	1596
387	1592
386	1588
385	1584
384	1580
383	1576
382	1572
381	1568
380	1564
379	1560
378	1556
377	1552
376	1548
375	1544
374	1540
373	1536
372	1532
371	1528
370	1524
369	1520
368	1516
367	1512
366	1508
365	1504
364	1500
363	1496
362	1492
361	1488
360	1484
359	1480
358	1476
357	1472
356	1468
355	1464
354	1460
353	1456
352	1452
351	1448
350	1444
349	1440
348	1436
347	1432
346	1428
345	1424
344	1420
343	1416
342	1412
341	1408
340	1404
339	1400
338	1396
337	1392
336	1388
335	1384
334	1380
333	1376
332	1372
331	1368
330	1364
329	1360
328	1356
327	1352
326	1348
325	1344
324	1340
323	1336
322	1332
321	1328
320	1324
319	1320
318	1316
317	1312
316	1308
315	1304
314	1300
313	1296
312	1292
311	1288
310	1284
309	1280
308	1276
307	1272
306	1268
305	1264
304	1260
303	1256
302	1252
301	1248
300	1244
299	1240
298	1236
297	1232
296	1228
295	1224
294	1220
293	1216
292	1212
291	1208
290	1204
289	1200
288	1196
287	1192
286	1188
285	1184
284	1180
283	1176
282	1172
281	1168
280	1164
279	1160
278	1156
277	1152
276	1148
275	1144
274	1140
273	1136
272	1132
271	1128
270	1124
269	1120
268	1116
267	1112
266	1108
265	1104
264	1100
263	1096
262	1092
261	1088
260	1084
259	1080
258	1076
257	1072
256	1068
255	1064
254	1060
253	1056
252	1052
251	1048
250	1044
249	1040
248	1036
247	1032
246	1028
245	1024
244	1020
243	1016
242	1012
241	1008
240	1004
239	1000
238	996
237	992
236	988
235	984
234	980
233	976
232	972
231	968
230	964
229	960
228	956
227	952
226	948
225	944
224	940
223	936
222	932
221	928
220	924
219	920
218	916
217	912
216	908
215	904
214	900
213	896
212	892
211	888
210	884
209	880
208	876
207	872
206	868
205	864
204	860
203	856
202	852
201	848
200	844
199	840
198	836
197	832
196	828
195	824
194	820
193	816
192	812
191	808
190	804
189	800
188	796
187	792
186	788
185	784
184	780
183	776
182	772
181	768
180	764
179	760
178	756
177	752
176	748
175	744
174	740
173	736
172	732
171	728
170	724
169	720
168	716
167	712
166	708
165	704
164	700
163	696
162	692
161	688
160	684
159	680
158	676
157	672
156	668
155	664
154	660
153	656
152	652
151	648
150	644
149	640
148	636
147	632
146	628
145	624
144	620
143	616
142	612
141	608
140	604
139	600
138	596
137	592
136	588
135	584
134	580
133	576
132	572
131	568
130	564
129	560
128	556
127	552
126	548
125	544
124	540
123	536
122	532
121	528
120	524
119	520
118	516
117	512
116	508
115	504
114	500
113	496
112	492
111	488
110	484
109	480
108	476
107	472
106	468
105	464
104	460
103	456
102	452
101	448
100	444
99	440
98	436
97	432
96	428
95	424
94	420
93	416
92	412
91	408
90	404
89	400
88	396
87	392
86	388
85	384
84	380
83	376
82	372
81	368
80	364
79	360
78	356
77	352
76	348
75	344
74	340
73	336
72	332
71	328
70	324
69	320
68	316
67	312
66	308
65	304
64	300
63	296
62	292
61	288
60	284
59	280
58	276
57	272
56	268
55	264
54	260
53	256
52	252
51	248
50	244
49	240
48	236
47	232
46	228
45	224
44	220
43	216
42	212
41	208
40	204
39	200
38	196
37	192
36	188
35	184
34	180
33	176
32	172
31	168
30	164
29	160
28	156
27	152
26	148
25	144
24	140
23	136
22	132
21	128
20	124
19	120
18	116
17	112
16	108
15	104
14	100
13	96
12	92
11	88
10	84
9	80
8	76
7	72
6	68
5	64
4	60
3	56
2	52
1	48
0	39