Details

sample753.0ms

Algorithm

intervals

Results

203.0ms	48×	body	2560	valid
151.0ms	89×	body	1280	valid
88.0ms	62×	body	640	valid
17.0ms	27×	body	320	valid
7.0ms	18×	body	160	valid
3.0ms	12×	body	80	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	6	276
1	13	276
2	17	276
3	19	276
done	19	276

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize73.0ms

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))

rewrite111.0ms

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:

66.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
21.0ms	(- x (sin x))

series310.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (- x (sin x)) (- x (tan x)))
107.0ms	(- x (tan x))
69.0ms	(- x (sin x))

simplify1.3s

Counts

89 → 89

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	157	37186
1	372	33919
2	1382	33799
done	5001	33599

prune465.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize31.0ms

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))

rewrite101.0ms

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)))
72.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
8.0ms	(- x (tan x))

series564.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (sin x) (- x (tan x)))
281.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
103.0ms	(- x (tan x))
83.0ms	(- x (tan x))

simplify1.5s

Counts

106 → 106

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	177	45270
1	389	39657
2	1452	39377
done	5000	39057

prune533.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

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))

rewrite48.0ms

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:

26.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
11.0ms	(- x (sin x))

series268.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(/ (- x (sin x)) (- x (tan x)))
85.0ms	(- x (tan x))
38.0ms	(- x (sin x))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	157	37186
1	372	33919
2	1382	33799
done	5001	33599

prune300.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

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)

rewrite80.0ms

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:

8.0ms	(- 9/40 (* (* x x) 27/2800))
50.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
19.0ms	(* (* x x) 27/2800)

series292.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(- 9/40 (* (* x x) 27/2800))
149.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
48.0ms	(* (* x x) 27/2800)

simplify1.7s

Counts

65 → 65

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	87	15274
1	258	11509
2	1743	11429
done	5002	11390

prune188.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes137.0ms

Accuracy

100% (0.0b remaining)

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

bsearch120.0ms

Steps

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

simplify10.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	20	741
1	25	741
done	25	741

end0.0ms

sample13.1s

Algorithm

intervals

Results

7.2s	1636×	body	2560	valid
3.6s	2687×	body	1280	valid
1.5s	1902×	body	640	valid
436.0ms	923×	body	320	valid
142.0ms	504×	body	160	valid
55.0ms	348×	body	80	valid