Details

sample504.0ms

Algorithm

intervals

Results

285.0ms	129×	body	1280	valid
109.0ms	62×	body	640	valid
33.0ms	256×	pre	80	true
16.0ms	21×	body	320	valid
15.0ms	36×	body	80	valid
5.0ms	8×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
113	2000
112	1986
111	1968
110	1953
109	1937
108	1917
107	1903
106	1888
105	1870
104	1854
103	1840
102	1823
101	1807
100	1791
99	1771
98	1756
97	1740
96	1720
95	1706
94	1691
93	1673
92	1657
91	1643
90	1626
89	1610
88	1594
87	1574
86	1559
85	1543
84	1521
83	1507
82	1492
81	1474
80	1458
79	1444
78	1427
77	1411
76	1395
75	1377
74	1362
73	1346
72	1324
71	1310
70	1295
69	1277
68	1261
67	1247
66	1230
65	1214
64	1198
63	1178
62	1163
61	1147
60	1127
59	1113
58	1098
57	1080
56	1064
55	1050
54	1033
53	1017
52	1001
51	983
50	968
49	952
48	932
47	918
46	903
45	885
44	869
43	855
42	838
41	822
40	806
39	786
38	771
37	755
36	733
35	719
34	704
33	686
32	670
31	656
30	639
29	623
28	607
27	587
26	572
25	556
24	534
23	520
22	505
21	487
20	471
19	457
18	440
17	424
16	408
15	386
14	370
13	360
12	330
11	270
10	178
9	126
8	93
7	78
6	58
5	46
4	35
3	29
2	22
1	15
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.2b	(tan (+ y z))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`tan-sum` `sum-log` `sub-neg` `diff-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 75

Calls

3 calls:

29.0ms	(+ x (- (tan (+ y z)) (tan a)))
16.0ms	(- (tan (+ y z)) (tan a))
5.0ms	(tan (+ y z))

series444.0ms

Counts

3 → 9

Calls

3 calls:

163.0ms	(+ x (- (tan (+ y z)) (tan a)))
210.0ms	(- (tan (+ y z)) (tan a))
71.0ms	(tan (+ y z))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	2004
3	2004
2	651
1	286
0	131

prune448.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))

rewrite615.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*l/`
16×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`frac-sub`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`flip3--` `flip--`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `associate-/r/` `-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `div-inv`

Counts

4 → 106

Calls

4 calls:

63.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
505.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
28.0ms	(* (tan y) (tan z))
16.0ms	(* (tan y) (tan z))

series1.6s

Counts

4 → 12

Calls

4 calls:

503.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
729.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
151.0ms	(* (tan y) (tan z))
188.0ms	(* (tan y) (tan z))

simplify1.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	2002
2	2002
1	700
0	209

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))
0.3b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b	(* (* (tan z) (tan y)) (* (tan z) (tan y)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
72×	`tan-quot`
36×	`frac-times` `pow-prod-down`
32×	`add-cbrt-cube` `add-exp-log`
24×	`associate-l/` `associate-r/`
18×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow-plus` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `swap-sqr` `unswap-sqr`

Counts

4 → 152

Calls

4 calls:

15.0ms	(* (tan y) (tan z))
14.0ms	(* (tan y) (tan z))
92.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
125.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))

series673.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (tan y) (tan z))
146.0ms	(* (tan y) (tan z))
176.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
188.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))

simplify1.3s

Counts

164 → 164

Iterations

Iter	Nodes
done	2002
3	2002
2	1754
1	506
0	170

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.3b	(* (tan y) (tan z))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `fma-def` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `associate-r` `associate-l`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 211

Calls

4 calls:

9.0ms	(+ (tan y) (tan z))
74.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
125.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
25.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

134.0ms	(+ (tan y) (tan z))
558.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
507.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
115.0ms	(* (tan y) (tan z))

simplify1.3s

Counts

223 → 223

Iterations

Iter	Nodes
done	2006
3	2006
2	1744
1	691
0	301

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes495.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample15.1s

Algorithm

intervals

Results

8.3s	3935×	body	1280	valid
4.0s	1981×	body	640	valid
954.0ms	8000×	pre	80	true
645.0ms	660×	body	320	valid
433.0ms	1137×	body	80	valid
168.0ms	287×	body	160	valid