Details

sample434.0ms

Algorithm

intervals

Results

127.0ms	48×	body	2560	valid
87.0ms	89×	body	1280	valid
55.0ms	27×	body	320	valid
34.0ms	62×	body	640	valid
4.0ms	18×	body	160	valid
2.0ms	12×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize52.0ms

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))

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

Counts

3 → 80

Calls

3 calls:

20.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
12.0ms	(- x (sin x))

series294.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (- x (sin x)) (- x (tan x)))
107.0ms	(- x (tan x))
64.0ms	(- x (sin x))

simplify1.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune408.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

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

Counts

4 → 94

Calls

4 calls:

13.0ms	(/ (sin x) (- x (tan x)))
94.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
9.0ms	(- x (tan x))
9.0ms	(- x (tan x))

series530.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (sin x) (- x (tan x)))
264.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
81.0ms	(- x (tan x))
70.0ms	(- x (tan x))

simplify1.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1452
1	389
0	177

prune539.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

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))

rewrite42.0ms

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`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

22.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series262.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(/ (- x (sin x)) (- x (tan x)))
95.0ms	(- x (tan x))
45.0ms	(- x (sin x))

simplify899.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune362.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* (* x x) 27/2800))
0.1b	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
0.2b	(* (* x x) 27/2800)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-l` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 56

Calls

3 calls:

7.0ms	(- 9/40 (* (* x x) 27/2800))
44.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
29.0ms	(* (* x x) 27/2800)

series291.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(- 9/40 (* (* x x) 27/2800))
125.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
61.0ms	(* (* x x) 27/2800)

simplify1.8s

Counts

65 → 65

Iterations

Iter	Nodes
done	5002
2	1743
1	258
0	87

prune180.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes79.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch97.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.02964489669427243
8	-0.9341403346610884	-0.003292329160956242	-0.029656023299900573

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample13.5s

Algorithm

intervals

Results

5.6s	1636×	body	2560	valid
5.2s	2687×	body	1280	valid
1.9s	1902×	body	640	valid
385.0ms	923×	body	320	valid
147.0ms	504×	body	160	valid
57.0ms	348×	body	80	valid