Details

sample183.0ms

Algorithm

intervals

Results

41.0ms	42×	body	10240	exit
38.0ms	43×	body	1280	valid
30.0ms	53×	body	640	valid
15.0ms	112×	body	80	valid
10.0ms	29×	body	320	valid
6.0ms	10×	body	320	nan
6.0ms	66×	body	80	nan
4.0ms	18×	body	160	valid
4.0ms	7×	body	640	nan
2.0ms	1×	body	2560	valid
2.0ms	4×	body	1280	nan
0.0ms	2×	body	160	nan

simplify8.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
144	4986
143	4970
142	4956
141	4939
140	4923
139	4907
138	4889
137	4874
136	4858
135	4836
134	4822
133	4807
132	4789
131	4773
130	4759
129	4742
128	4726
127	4710
126	4690
125	4675
124	4659
123	4641
122	4627
121	4612
120	4594
119	4578
118	4564
117	4547
116	4531
115	4515
114	4495
113	4480
112	4464
111	4444
110	4430
109	4415
108	4397
107	4381
106	4367
105	4350
104	4334
103	4318
102	4298
101	4283
100	4267
99	4245
98	4231
97	4216
96	4198
95	4182
94	4168
93	4151
92	4135
91	4119
90	4103
89	4088
88	4072
87	4050
86	4036
85	4021
84	4003
83	3987
82	3973
81	3956
80	3940
79	3924
78	3906
77	3891
76	3875
75	3853
74	3839
73	3824
72	3806
71	3790
70	3776
69	3759
68	3743
67	3727
66	3707
65	3692
64	3676
63	3654
62	3640
61	3625
60	3607
59	3591
58	3577
57	3560
56	3544
55	3528
54	3508
53	3493
52	3477
51	3455
50	3441
49	3426
48	3408
47	3392
46	3378
45	3361
44	3345
43	3329
42	3309
41	3294
40	3278
39	3260
38	3246
37	3231
36	3213
35	3197
34	3183
33	3166
32	3150
31	3134
30	3114
29	3099
28	3083
27	3061
26	3047
25	3032
24	3014
23	2998
22	2984
21	2967
20	2951
19	2935
18	2915
17	2900
16	2884
15	2866
14	2822
13	2455
12	2112
11	1738
10	1224
9	862
8	678
7	469
6	261
5	107
4	66
3	48
2	33
1	20
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
2.9b	(+ (- 1.0 y) (* y (exp z)))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
10×	`add-exp-log`
9×	`add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out`
7×	`log-prod` `associate-l`
5×	`log-pow`
4×	`log-div` `insert-posit16` `associate-/l*` `distribute-lft-out--`
3×	`associate-/r` `flip3-+` `associate-r*` `flip-+`
2×	`associate-+l+` `sum-log` `div-sub` `prod-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `*-commutative` `associate-+l-` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

21.0ms	(* y (exp z))
107.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
41.0ms	(log (+ (- 1.0 y) (* y (exp z))))
71.0ms	(+ (- 1.0 y) (* y (exp z)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* y (exp z))
251.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
119.0ms	(log (+ (- 1.0 y) (* y (exp z))))
64.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify3.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
3	4810
2	1345
1	466
0	203

prune664.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 1.0) (* (* z z) 0.5))
0.0b	(* (* z z) 0.5)
2.1b	(* y (+ (* z 1.0) (* (* z z) 0.5)))
5.5b	(/ (+ (log 1.0) (* y (+ (* z 1.0) (* (* z z) 0.5)))) t)

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
65×	`associate-l`
42×	`add-sqr-sqrt`
38×	`distribute-lft-out`
28×	`add-cube-cbrt`
24×	`associate-r`
21×	`times-frac`
19×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
8×	`log-pow` `unswap-sqr`
7×	`associate-/l*`
6×	`*-commutative` `add-log-exp`
4×	`swap-sqr` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`+-commutative` `associate-/r*` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 143

Calls

4 calls:

106.0ms	(+ (* z 1.0) (* (* z z) 0.5))
46.0ms	(* (* z z) 0.5)
330.0ms	(* y (+ (* z 1.0) (* (* z z) 0.5)))
2.4s	(/ (+ (log 1.0) (* y (+ (* z 1.0) (* (* z z) 0.5)))) t)

series470.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (* z 1.0) (* (* z z) 0.5))
54.0ms	(* (* z z) 0.5)
120.0ms	(* y (+ (* z 1.0) (* (* z z) 0.5)))
178.0ms	(/ (+ (log 1.0) (* y (+ (* z 1.0) (* (* z z) 0.5)))) t)

simplify2.0s

Counts

155 → 155

Iterations

Iter	Nodes
done	5003
2	1901
1	522
0	190

prune908.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.6b	(cbrt z)
5.5b	(/ (+ (log 1.0) (* (* y (* (cbrt z) (cbrt z))) (+ (* (cbrt z) 1.0) (* (* (cbrt z) z) 0.5)))) t)

rewrite4.4s

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
27×	`times-frac`
24×	`associate-l` `distribute-lft-out`
21×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`pow1`
12×	`log-pow`
9×	`cbrt-prod` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r*` `pow1/3`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
1.0ms	(cbrt z)
4.4s	(/ (+ (log 1.0) (* (* y (* (cbrt z) (cbrt z))) (+ (* (cbrt z) 1.0) (* (* (cbrt z) z) 0.5)))) t)

series1.1s

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt z)
288.0ms	(cbrt z)
243.0ms	(cbrt z)
241.0ms	(/ (+ (log 1.0) (* (* y (* (cbrt z) (cbrt z))) (+ (* (cbrt z) 1.0) (* (* (cbrt z) z) 0.5)))) t)

simplify4.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5104
3	4472
2	828
1	237
0	104

prune606.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
5.5b	(/ (+ (log 1.0) (* (* y (* (cbrt z) (cbrt z))) (+ (* (cbrt z) 1.0) (* (* (posit16->real (real->posit16 (cbrt z))) z) 0.5)))) t)
57.6b	(posit16->real (real->posit16 (cbrt z)))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
27×	`times-frac`
24×	`associate-l` `distribute-lft-out`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`pow1`
12×	`log-pow`
9×	`associate-/l*`
6×	`cbrt-prod` `add-cbrt-cube` `add-exp-log`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r*`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `remove-posit16`

Counts

4 → 87

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
3.3s	(/ (+ (log 1.0) (* (* y (* (cbrt z) (cbrt z))) (+ (* (cbrt z) 1.0) (* (* (posit16->real (real->posit16 (cbrt z))) z) 0.5)))) t)
11.0ms	(posit16->real (real->posit16 (cbrt z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt z)
280.0ms	(cbrt z)
225.0ms	(/ (+ (log 1.0) (* (* y (* (cbrt z) (cbrt z))) (+ (* (cbrt z) 1.0) (* (* (posit16->real (real->posit16 (cbrt z))) z) 0.5)))) t)
263.0ms	(posit16->real (real->posit16 (cbrt z)))

simplify3.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
3	4560
2	851
1	249
0	113

prune785.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

regimes1.3s

Accuracy

69.9% (4.7b remaining)

Error of 8.9b against oracle of 4.2b and baseline of 19.8b

bsearch916.0ms

Steps

Iters	Range		Point
6	6.504303590374269e-18	1.0253848516655035e-16	9.047911306874446e-17
9	2.1987480550803053e-111	4.680582706131457e-106	1.6081434733570535e-109
8	-2.702077193721847e-92	-4.047764226026223e-95	-7.588076395555027e-93
10	-1395.513557668287	-2.0438040903403646e-10	-6.220564919949488e-06

simplify31.0ms

Iterations

Iter	Nodes
done	67
3	67
2	64
1	61
0	46

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.5s	1523×	body	10240	exit
1.7s	1468×	body	1280	valid
1.2s	1580×	body	640	valid
666.0ms	3506×	body	80	valid
533.0ms	264×	body	640	nan
430.0ms	900×	body	320	valid
283.0ms	98×	body	2560	valid
281.0ms	2466×	body	80	nan
129.0ms	479×	body	160	valid
78.0ms	108×	body	1280	nan
69.0ms	197×	body	320	nan
25.0ms	116×	body	160	nan