Details

sample543.0ms

Algorithm

intervals

Results

114.0ms	44×	body	2560	valid
50.0ms	77×	body	1280	valid
44.0ms	65×	body	640	valid
8.0ms	38×	body	320	valid
3.0ms	17×	body	80	valid
2.0ms	15×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5
done	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (sin x))
1.0b	(- x (tan x))

rewrite41.0ms

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:

23.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (sin x))
8.0ms	(- x (tan x))

series186.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- x (sin x)) (- x (tan x)))
33.0ms	(- x (sin x))
72.0ms	(- x (tan x))

simplify150.0ms

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685
done	5001	685

prune201.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.0b	(- x (tan x))
1.0b	(- x (tan x))

rewrite107.0ms

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:

14.0ms	(/ (sin x) (- x (tan x)))
79.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series346.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (sin x) (- x (tan x)))
177.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
51.0ms	(- x (tan x))
55.0ms	(- x (tan x))

simplify38.0ms

Counts

106 → 106

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872
done	5001	872

prune241.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.0b	(- x (tan x))
1.0b	(- x (tan x))

rewrite104.0ms

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:

14.0ms	(/ (sin x) (- x (tan x)))
76.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series353.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (sin x) (- x (tan x)))
184.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
56.0ms	(- x (tan x))
55.0ms	(- x (tan x))

simplify44.0ms

Counts

106 → 106

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	872
2	5001	872
done	5001	872

prune292.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(- x (tan x))
1.0b	(- x (tan x))
1.0b	(- x (tan x))
1.0b	(- x (tan x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

5.0ms	(- x (tan x))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- x (tan x))
57.0ms	(- x (tan x))
51.0ms	(- x (tan x))
57.0ms	(- x (tan x))

simplify152.0ms

Counts

68 → 68

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	91	324
1	200	304
2	471	304
3	1247	304
4	4646	304
5	5001	304
done	5001	304

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch87.0ms

Steps

Iters	Range		Point
8	0.016621422887445694	5.276955647516397	0.06543863896081262
9	-0.05800990145057735	-1.1864783425707322e-08	-0.031511785901855695

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50
done	45	50

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1613×	body	2560	valid
1.8s	2704×	body	1280	valid
682.0ms	1926×	body	640	valid
218.0ms	934×	body	320	valid
72.0ms	475×	body	160	valid
31.0ms	348×	body	80	valid