Details

sample559.0ms

Algorithm

intervals

Results

156.0ms	60×	body	2560	valid
67.0ms	103×	body	1280	valid
15.0ms	47×	body	640	valid
6.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	11×	body	80	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: 31.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.6b	(- x (tan x))
0.6b	(- x (sin x))

rewrite56.0ms

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:

34.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
61.0ms	(- x (tan x))
43.0ms	(- x (sin x))

simplify54.0ms

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune247.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- x (tan x))
0.6b	(- x (tan x))
0.6b	(- x (sin x))
0.6b	(- x (sin x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

7.0ms	(- x (tan x))
6.0ms	(- x (tan x))
7.0ms	(- x (sin x))
8.0ms	(- x (sin x))

series175.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- x (tan x))
54.0ms	(- x (tan x))
32.0ms	(- x (sin x))
36.0ms	(- x (sin x))

simplify93.0ms

Counts

124 → 124

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	258	974
1	749	610
2	3295	574
3	5001	406
done	5001	406

prune277.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
18.8b	(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)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(fma 27/2800 (pow x 4) 1/2)
47.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify144.0ms

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

prune72.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fma 27/2800 (pow x 4) 1/2) 3)
0.0b	(fma 27/2800 (pow x 4) 1/2)
5.4b	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
18.8b	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

3.0ms	(pow (fma 27/2800 (pow x 4) 1/2) 3)
0.0ms	(fma 27/2800 (pow x 4) 1/2)
3.0ms	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
0.0ms	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow (fma 27/2800 (pow x 4) 1/2) 3)
86.0ms	(fma 27/2800 (pow x 4) 1/2)
86.0ms	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
46.0ms	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

simplify189.0ms

Counts

80 → 80

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	170	394
1	637	363
2	4312	356
3	5001	356
done	5001	356

prune183.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes64.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch78.0ms

Steps

Iters	Range		Point
8	0.02319676823116778	7.055123656280252	1.5807919572689517
10	-1.8070707071506563e+17	-0.15939393977811658	-1.5845262208940065

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18
done	27	18

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.5s	1575×	body	2560	valid
1.9s	2776×	body	1280	valid
681.0ms	1962×	body	640	valid
207.0ms	904×	body	320	valid
68.0ms	439×	body	160	valid
31.0ms	344×	body	80	valid