Details

sample230.0ms

Algorithm

intervals

Results

91.0ms	45×	body	2560	valid
80.0ms	88×	body	1280	valid
26.0ms	54×	body	640	valid
11.0ms	34×	body	320	valid
5.0ms	21×	body	160	valid
2.0ms	14×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.4b	(- 1.0 (cos x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

59.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series82.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	106	665
1	235	645
2	531	609
3	1194	609
4	3136	608
done	5000	608

prune228.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.4b	(- 1.0 (cos x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

33.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
23.0ms	(/ (sin x) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series142.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
61.0ms	(/ (sin x) (- 1.0 (cos x)))
30.0ms	(- 1.0 (cos x))

simplify2.3s

Counts

168 → 168

Iterations

Useful iterations: 3 (933.0ms)

Iter	Nodes	Cost
0	239	2702
1	499	2361
2	1054	2144
3	2568	2092
done	5000	2092

prune348.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- 1.0 (cos x)))
0.2b	(/ (log (exp (- 1.0 (cos x)))) (sin x))
2.4b	(- 1.0 (cos x))
2.5b	(log (exp (- 1.0 (cos x))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`exp-prod` `log-pow`
27×	`times-frac`
25×	`add-cube-cbrt`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod`
4×	`exp-sum`
3×	`sub-neg` `exp-diff` `associate-/r*`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 103

Calls

4 calls:

18.0ms	(exp (- 1.0 (cos x)))
107.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
6.0ms	(- 1.0 (cos x))
16.0ms	(log (exp (- 1.0 (cos x))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(exp (- 1.0 (cos x)))
73.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
21.0ms	(- 1.0 (cos x))
35.0ms	(log (exp (- 1.0 (cos x))))

simplify3.1s

Counts

115 → 115

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	160	1341
1	287	1132
2	637	1070
3	1433	1070
4	4019	1069
done	5000	1069

prune319.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
2.5b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`times-frac`
21×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 77

Calls

3 calls:

6.0ms	(/ 1.0 (sin x))
10.0ms	(/ (cos x) (sin x))
69.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series214.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1.0 (sin x))
40.0ms	(/ (cos x) (sin x))
138.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify3.2s

Counts

86 → 86

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	146	963
1	289	920
2	619	873
3	1341	873
4	3393	870
done	5001	870

prune275.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.1b

regimes162.0ms

Accuracy

97.9% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.3b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	53
1	37	45
done	37	45

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.0s	1534×	body	2560	valid
2.2s	2826×	body	1280	valid
1.7s	1863×	body	640	valid
365.0ms	956×	body	320	valid
124.0ms	458×	body	160	valid
36.0ms	359×	body	80	valid
18.0ms	4×	body	5120	valid