Details

sample696.0ms

Algorithm

intervals

Results

317.0ms	65×	body	2560	valid
189.0ms	84×	body	1280	valid
66.0ms	56×	body	640	valid
21.0ms	27×	body	320	valid
9.0ms	17×	body	160	valid
2.0ms	7×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

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

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))

rewrite46.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

22.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
13.0ms	(- x (sin x))

series242.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (- x (sin x)) (- x (tan x)))
76.0ms	(- x (tan x))
54.0ms	(- x (sin x))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	2010
3	2010
2	964
1	375
0	160

prune340.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) 9/40)
0.1b	(* (* (* x x) (* x x)) 27/2800)
0.1b	(* (* x x) (* x x))
16.6b	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

138×	`pow1`
39×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
36×	`pow-prod-up`
24×	`prod-exp` `cbrt-unprod`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
9×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`diff-log` `associate-l` `*-commutative` `unswap-sqr`
2×	`sub-neg` `associate--l+`
1×	`associate--l-` `flip3--` `swap-sqr` `flip--`

Counts

4 → 130

Calls

4 calls:

14.0ms	(* (* x x) 9/40)
84.0ms	(* (* (* x x) (* x x)) 27/2800)
32.0ms	(* (* x x) (* x x))
153.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

series246.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* x x) 9/40)
72.0ms	(* (* (* x x) (* x x)) 27/2800)
44.0ms	(* (* x x) (* x x))
81.0ms	(- (- (* (* x x) 9/40) 1/2) (* (* (* x x) (* x x)) 27/2800))

simplify1.1s

Counts

142 → 142

Iterations

Iter	Nodes
done	2009
3	2009
2	1164
1	397
0	135

prune291.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

2.0b	(- x (tan x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

4.0ms	(- x (tan x))
5.0ms	(- x (sin x))
15.0ms	(- x (sin x))
11.0ms	(- x (sin x))

series251.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- x (tan x))
63.0ms	(- x (sin x))
47.0ms	(- x (sin x))
40.0ms	(- x (sin x))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
5	2000
4	1619
3	720
2	357
1	155
0	78

prune367.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes150.0ms

Accuracy

100% (0.0b remaining)

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

bsearch213.0ms

Steps

Iters	Range		Point
10	3.4946005567744297e-15	48819.349325626084	0.025242037778536456
9	-6838974.188497498	-0.005838610583870787	-0.028431537088381868

simplify8.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample15.8s

Algorithm

intervals

Results

6.6s	1668×	body	2560	valid
5.6s	2722×	body	1280	valid
2.4s	1894×	body	640	valid
692.0ms	905×	body	320	valid
293.0ms	484×	body	160	valid
75.0ms	327×	body	80	valid