Details

sample429.0ms

Algorithm

intervals

Results

90.0ms	44×	body	2560	valid
57.0ms	87×	body	1280	valid
19.0ms	54×	body	640	valid
7.0ms	32×	body	320	valid
6.0ms	25×	body	160	valid
1.0ms	14×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series182.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
44.0ms	(- x (sin x))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	959	1147
3	2670	1147
done	5000	1145

prune213.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b	(- x (tan x))
1.4b	(- x (tan x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

7.0ms	(/ (sin x) (- x (tan x)))
53.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series363.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (sin x) (- x (tan x)))
186.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
58.0ms	(- x (tan x))
55.0ms	(- x (tan x))

simplify1.4s

Counts

106 → 106

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	177	1565
1	377	1511
2	1022	1449
3	3660	1445
done	5000	1444

prune266.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b	(- x (tan x))
1.4b	(- x (tan x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

7.0ms	(/ (sin x) (- x (tan x)))
53.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (sin x) (- x (tan x)))
187.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
57.0ms	(- x (tan x))
55.0ms	(- x (tan x))

simplify1.5s

Counts

106 → 106

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	177	1565
1	377	1511
2	1022	1449
3	3660	1445
done	5000	1444

prune323.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- x (tan x))
1.4b	(- x (tan x))
1.4b	(- x (tan x))
1.4b	(- (pow (/ x (- x (tan x))) 3) (pow (/ (sin x) (- x (tan x))) 3))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
80×	`times-frac`
68×	`unpow-prod-down` `cube-prod`
52×	`distribute-lft-out--`
47×	`difference-of-squares`
16×	`associate-/r/`
12×	`add-cube-cbrt` `flip3--` `distribute-rgt-out--` `flip--` `add-log-exp` `sqr-pow`
8×	`div-inv`
4×	`pow1` `add-exp-log` `cube-div` `sub-neg` `diff-log` `add-cbrt-cube`
1×	`difference-cubes` `frac-sub` `sub-div`

Counts

4 → 138

Calls

4 calls:

3.0ms	(- x (tan x))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))
179.0ms	(- (pow (/ x (- x (tan x))) 3) (pow (/ (sin x) (- x (tan x))) 3))

series423.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- x (tan x))
53.0ms	(- x (tan x))
60.0ms	(- x (tan x))
250.0ms	(- (pow (/ x (- x (tan x))) 3) (pow (/ (sin x) (- x (tan x))) 3))

simplify589.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (171.0ms)

Iter	Nodes	Cost
0	181	3356
1	475	3214
2	1548	3160
done	5000	3160

prune424.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch107.0ms

Steps

Iters	Range		Point
9	3.182061564411226e-09	0.0591185632533196	0.028578832745905277
8	-0.04390830018224924	-1.7961213486546931e-06	-0.02915897731694385

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	154
1	50	154
done	50	154

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1620×	body	2560	valid
1.8s	2690×	body	1280	valid
662.0ms	1887×	body	640	valid
223.0ms	951×	body	320	valid
74.0ms	476×	body	160	valid
39.0ms	376×	body	80	valid