Details

sample699.0ms

Algorithm

intervals

Results

202.0ms	42×	body	2560	valid
129.0ms	86×	body	1280	valid
85.0ms	18×	body	160	valid
63.0ms	64×	body	640	valid
19.0ms	35×	body	320	valid
2.0ms	11×	body	80	valid

simplify42.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (sin x))

rewrite131.0ms

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:

86.0ms	(/ (- x (sin x)) (- x (tan x)))
14.0ms	(- x (tan x))
21.0ms	(- x (sin x))

series426.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(/ (- x (sin x)) (- x (tan x)))
182.0ms	(- x (tan x))
82.0ms	(- x (sin x))

simplify4.7s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	4728
2	1274
1	500
0	209

prune742.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite421.0ms

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:

37.0ms	(/ (sin x) (- x (tan x)))
239.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
14.0ms	(- x (tan x))
16.0ms	(- x (tan x))

series686.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (sin x) (- x (tan x)))
331.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
99.0ms	(- x (tan x))
124.0ms	(- x (tan x))

simplify4.4s

Counts

600 → 600

Iterations

Iter	Nodes
done	5000
2	3373
1	1401
0	617

prune4.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize81.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (tan x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite67.0ms

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:

15.0ms	(- x (tan x))
15.0ms	(- x (tan x))
15.0ms	(- x (tan x))
15.0ms	(- x (tan x))

series408.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- x (tan x))
103.0ms	(- x (tan x))
98.0ms	(- x (tan x))
116.0ms	(- x (tan x))

simplify4.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
4	2649
3	958
2	362
1	162
0	73

prune853.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.3b	(- x (tan x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

35.0ms	(/ (sin x) (- x (tan x)))
14.0ms	(- x (tan x))
15.0ms	(- x (tan x))
15.0ms	(- x (tan x))

series450.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (sin x) (- x (tan x)))
92.0ms	(- x (tan x))
104.0ms	(- x (tan x))
127.0ms	(- x (tan x))

simplify3.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5052
3	3471
2	889
1	308
0	143

prune922.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes85.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch183.0ms

Steps

Iters	Range		Point
9	2.490703692944805e-05	37.746059492850215	1.5845235347277338
9	-1.440408271564231	-1.963203309137196e-05	-0.03414424847811019

simplify12.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample19.5s

Algorithm

intervals

Results

7.7s	1611×	body	2560	valid
7.2s	2719×	body	1280	valid
2.1s	1852×	body	640	valid
1.0s	382×	body	80	valid
898.0ms	950×	body	320	valid
181.0ms	486×	body	160	valid