Details

sample531.0ms

Algorithm

intervals

Results

105.0ms	52×	body	2560	valid
81.0ms	92×	body	1280	valid
19.0ms	57×	body	640	valid
7.0ms	34×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	7×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 31.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

32.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify55.0ms

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854
done	5001	854

prune230.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.6b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

16.0ms	(/ (sin x) (- x (tan x)))
109.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (sin x) (- x (tan x)))
173.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
55.0ms	(- x (tan x))
51.0ms	(- x (tan x))

simplify197.0ms

Counts

600 → 600

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1359	22035
1	3883	15840
2	5001	15776
done	5001	15776

prune957.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

28.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series165.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
32.0ms	(- x (sin x))

simplify57.0ms

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854
done	5001	854

prune211.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
17.6b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series134.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(fma 27/2800 (pow x 4) 1/2)
49.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify143.0ms

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117
done	5001	117

prune64.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch77.0ms

Steps

Iters	Range		Point
10	0.00012253353073063669	15794870057.515802	0.02672696280496189
9	-2.7342232818785663	-5.599255928070541e-06	-0.029514586132827595

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	18
1	25	18
done	25	18

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1634×	body	2560	valid
1.9s	2798×	body	1280	valid
608.0ms	1811×	body	640	valid
195.0ms	914×	body	320	valid
77.0ms	490×	body	160	valid
45.0ms	353×	body	80	valid