Details

sample164.0ms

Algorithm

intervals

Results

41.0ms	55×	body	1280	valid
34.0ms	47×	body	10240	exit
20.0ms	52×	body	640	valid
15.0ms	76×	body	80	nan
9.0ms	103×	body	80	valid
8.0ms	31×	body	320	valid
5.0ms	3×	body	2560	valid
2.0ms	10×	body	640	nan
2.0ms	14×	body	160	valid
2.0ms	5×	body	1280	nan
2.0ms	9×	body	320	nan
0.0ms	4×	body	160	nan

simplify17.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
230	4994
229	4969
228	4959
227	4946
226	4940
225	4919
224	4909
223	4892
222	4886
221	4861
220	4855
219	4842
218	4836
217	4815
216	4805
215	4788
214	4782
213	4757
212	4751
211	4738
210	4732
209	4711
208	4701
207	4684
206	4678
205	4653
204	4647
203	4634
202	4628
201	4607
200	4597
199	4580
198	4574
197	4549
196	4541
195	4528
194	4522
193	4501
192	4495
191	4478
190	4472
189	4447
188	4441
187	4428
186	4422
185	4401
184	4391
183	4374
182	4368
181	4343
180	4337
179	4324
178	4318
177	4297
176	4289
175	4272
174	4266
173	4241
172	4235
171	4222
170	4216
169	4195
168	4185
167	4168
166	4162
165	4137
164	4131
163	4118
162	4112
161	4091
160	4083
159	4066
158	4060
157	4035
156	4025
155	4012
154	4006
153	3985
152	3975
151	3958
150	3952
149	3927
148	3917
147	3904
146	3898
145	3877
144	3871
143	3854
142	3848
141	3823
140	3813
139	3800
138	3794
137	3773
136	3767
135	3750
134	3744
133	3719
132	3711
131	3698
130	3692
129	3671
128	3663
127	3646
126	3640
125	3615
124	3605
123	3592
122	3586
121	3565
120	3559
119	3542
118	3536
117	3511
116	3501
115	3488
114	3482
113	3461
112	3453
111	3436
110	3430
109	3405
108	3395
107	3382
106	3376
105	3355
104	3345
103	3328
102	3322
101	3297
100	3291
99	3278
98	3272
97	3251
96	3241
95	3224
94	3218
93	3193
92	3185
91	3172
90	3166
89	3145
88	3137
87	3120
86	3114
85	3089
84	3083
83	3070
82	3064
81	3043
80	3033
79	3016
78	3010
77	2985
76	2979
75	2966
74	2960
73	2939
72	2933
71	2916
70	2910
69	2885
68	2877
67	2864
66	2858
65	2837
64	2827
63	2810
62	2804
61	2779
60	2771
59	2758
58	2752
57	2731
56	2723
55	2706
54	2700
53	2675
52	2669
51	2656
50	2650
49	2629
48	2619
47	2602
46	2596
45	2571
44	2565
43	2552
42	2546
41	2525
40	2517
39	2500
38	2494
37	2469
36	2461
35	2448
34	2442
33	2421
32	2413
31	2396
30	2390
29	2365
28	2359
27	2346
26	2340
25	2319
24	2309
23	2292
22	2286
21	2261
20	2253
19	2240
18	2234
17	2213
16	2187
15	2170
14	2164
13	2139
12	2095
11	1735
10	1206
9	788
8	572
7	448
6	253
5	127
4	77
3	53
2	35
1	20
0	12

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
2.6b	(log (fma (expm1 z) y 1.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
17×	`pow1`
14×	`log-pow`
6×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `associate-/r*` `fma-neg` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `rem-log-exp` `flip--` `distribute-lft-out--`

Counts

3 → 115

Calls

3 calls:

20.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
12.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
1.0ms	(log (fma (expm1 z) y 1.0))

series340.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
165.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
67.0ms	(log (fma (expm1 z) y 1.0))

simplify1.9s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1693
1	617
0	250

prune703.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0)))
2.6b	(log (fma (expm1 z) y 1.0))
2.6b	(log (fma (expm1 z) y 1.0))
2.6b	(log (fma (expm1 z) y 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
15×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`add-exp-log` `log-pow`
6×	`add-cbrt-cube` `swap-sqr`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `rem-log-exp`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

8.0ms	(* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0)))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))

series334.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (log (fma (expm1 z) y 1.0)) (log (fma (expm1 z) y 1.0)))
71.0ms	(log (fma (expm1 z) y 1.0))
81.0ms	(log (fma (expm1 z) y 1.0))
76.0ms	(log (fma (expm1 z) y 1.0))

simplify1.8s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1431
1	432
0	141

prune749.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.6b	(log (fma (expm1 z) y 1.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `pow1/3`
1×	`rem-log-exp` `log-pow`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(log (fma (expm1 z) y 1.0))

series818.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(cbrt x)
228.0ms	(cbrt x)
262.0ms	(cbrt x)
72.0ms	(log (fma (expm1 z) y 1.0))

simplify1.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	1623
2	508
1	188
0	88

prune529.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (log (fma (expm1 z) y 1.0))) t)
0.1b	(* (sqrt (log (fma (expm1 z) y 1.0))) (/ (sqrt (log (fma (expm1 z) y 1.0))) t))
2.6b	(log (fma (expm1 z) y 1.0))
2.6b	(log (fma (expm1 z) y 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
37×	`sqrt-prod`
25×	`associate-r`
16×	`pow1`
13×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`log-pow`
7×	`associate-l` `associate-/l*`
6×	`log-prod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `div-exp` `rem-log-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 127

Calls

4 calls:

6.0ms	(/ (sqrt (log (fma (expm1 z) y 1.0))) t)
20.0ms	(* (sqrt (log (fma (expm1 z) y 1.0))) (/ (sqrt (log (fma (expm1 z) y 1.0))) t))
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))

series846.0ms

Counts

4 → 12

Calls

4 calls:

507.0ms	(/ (sqrt (log (fma (expm1 z) y 1.0))) t)
181.0ms	(* (sqrt (log (fma (expm1 z) y 1.0))) (/ (sqrt (log (fma (expm1 z) y 1.0))) t))
71.0ms	(log (fma (expm1 z) y 1.0))
86.0ms	(log (fma (expm1 z) y 1.0))

simplify1.7s

Counts

139 → 139

Iterations

Iter	Nodes
done	5002
2	1607
1	511
0	211

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.8b

regimes840.0ms

Accuracy

46% (4.2b remaining)

Error of 8.0b against oracle of 3.7b and baseline of 11.6b

bsearch244.0ms

Steps

Iters	Range		Point
8	1.5544988602664075e-89	1.5773640188552697e-86	2.8447097992841593e-88
7	-1.7206091677840204e-53	-3.02122600279542e-55	-3.887828973606996e-55

simplify13.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample7.1s

Algorithm

intervals

Results

1.8s	1444×	body	1280	valid
1.7s	1538×	body	10240	exit
947.0ms	1584×	body	640	valid
944.0ms	3526×	body	80	valid
306.0ms	919×	body	320	valid
271.0ms	2502×	body	80	nan
165.0ms	83×	body	2560	valid
121.0ms	476×	body	160	valid
99.0ms	256×	body	640	nan
67.0ms	127×	body	1280	nan
48.0ms	185×	body	320	nan
18.0ms	108×	body	160	nan