Details

sample521.0ms

Algorithm

intervals

Results

272.0ms	59×	body	2560	valid
100.0ms	91×	body	1280	valid
41.0ms	58×	body	640	valid
9.0ms	21×	body	320	valid
4.0ms	12×	body	160	valid
3.0ms	15×	body	80	valid

simplify23.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.5b	(- x (tan x))
1.6b	(- x (sin x))

rewrite81.0ms

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:

37.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series265.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(/ (- x (sin x)) (- x (tan x)))
73.0ms	(- x (tan x))
58.0ms	(- x (sin x))

simplify2.5s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	157	37186
1	372	33919
2	952	33719
3	3260	33639
done	5006	33639

prune404.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (* (* x x) (* x x)))
0.1b	(* (* x x) (* x x))
0.1b	(* 9/40 (* x x))
18.1b	(- (* 9/40 (* x x)) (+ 1/2 (* 27/2800 (* (* x x) (* x x)))))

rewrite219.0ms

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-l`
6×	`*-un-lft-identity` `add-cube-cbrt`
3×	`associate-r` `*-commutative` `unswap-sqr`
2×	`diff-log`
1×	`sum-log` `sub-neg` `flip3--` `swap-sqr` `flip--` `associate--r+`

Counts

4 → 124

Calls

4 calls:

110.0ms	(* 27/2800 (* (* x x) (* x x)))
45.0ms	(* (* x x) (* x x))
28.0ms	(* 9/40 (* x x))
31.0ms	(- (* 9/40 (* x x)) (+ 1/2 (* 27/2800 (* (* x x) (* x x)))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* 27/2800 (* (* x x) (* x x)))
54.0ms	(* (* x x) (* x x))
34.0ms	(* 9/40 (* x x))
76.0ms	(- (* 9/40 (* x x)) (+ 1/2 (* 27/2800 (* (* x x) (* x x)))))

simplify2.1s

Counts

136 → 136

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	125	23621
1	387	17115
2	1340	15880
done	5000	15840

prune283.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

8.0ms	(- 9/40 (* 27/2800 (* x x)))
45.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
26.0ms	(* 27/2800 (* x x))

series282.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(- 9/40 (* 27/2800 (* x x)))
156.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
50.0ms	(* 27/2800 (* x x))

simplify4.9s

Counts

65 → 65

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	86	15234
1	264	11510
2	890	11350
3	4168	11230
done	5000	11230

prune201.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

1.5b	(- x (tan x))
1.6b	(- x (sin x))
1.6b	(- x (sin x))
1.6b	(- x (sin x))

rewrite26.0ms

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` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

8.0ms	(- x (tan x))
6.0ms	(- x (sin x))
5.0ms	(- x (sin x))
5.0ms	(- x (sin x))

series232.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- x (tan x))
58.0ms	(- x (sin x))
45.0ms	(- x (sin x))
53.0ms	(- x (sin x))

simplify3.6s

Counts

68 → 68

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	76	17703
1	153	15695
2	355	15655
3	722	15655
4	1643	15655
5	4534	15655
done	5048	15655

prune342.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch116.0ms

Steps

Iters	Range		Point
9	5.312512837176874e-08	0.1909160003853501	0.027937497485642955
7	-0.18371106458419734	-0.0075399940621682995	-0.030218439026609593

simplify14.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	23	901
1	30	901
done	30	901

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.1s	1567×	body	2560	valid
4.4s	2839×	body	1280	valid
2.1s	1839×	body	640	valid
503.0ms	930×	body	320	valid
198.0ms	470×	body	160	valid
60.0ms	355×	body	80	valid