Details

sample137.0ms

Algorithm

intervals

Results

68.0ms	49×	body	2560	valid
42.0ms	91×	body	1280	valid
12.0ms	54×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	14×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4
done	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify78.0ms

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373
done	5001	373

prune143.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

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)))

rewrite53.0ms

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))
35.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series126.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1.0 (sin x))
19.0ms	(/ (cos x) (sin x))
83.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify56.0ms

Counts

86 → 86

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	287	581
1	772	552
2	2229	552
3	5002	551
done	5002	551

prune194.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin x))
0.1b	(/ 1.0 (sin x))
0.2b	(* (cos x) (/ 1 (sin x)))
2.5b	(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`associate-r` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`div-exp`
4×	`prod-exp` `div-inv`
3×	`cbrt-undiv` `associate-r/` `associate-l*` `un-div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub` `cbrt-unprod` `sub-div`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `flip--` `inv-pow`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ 1 (sin x))
5.0ms	(/ 1.0 (sin x))
18.0ms	(* (cos x) (/ 1 (sin x)))
28.0ms	(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

series141.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (sin x))
24.0ms	(/ 1.0 (sin x))
19.0ms	(* (cos x) (/ 1 (sin x)))
83.0ms	(- (/ 1.0 (sin x)) (* (cos x) (/ 1 (sin x))))

simplify95.0ms

Counts

123 → 123

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	391	701
1	1433	627
2	4833	581
3	5002	577
done	5002	577

prune217.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos x) (sin x))
0.3b	(exp (- (/ 1.0 (sin x)) (/ (cos x) (sin x))))
1.7b	(log (exp (- (/ 1.0 (sin x)) (/ (cos x) (sin x)))))
2.5b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

9.0ms	(/ (cos x) (sin x))
86.0ms	(exp (- (/ 1.0 (sin x)) (/ (cos x) (sin x))))
91.0ms	(log (exp (- (/ 1.0 (sin x)) (/ (cos x) (sin x)))))
32.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (cos x) (sin x))
85.0ms	(exp (- (/ 1.0 (sin x)) (/ (cos x) (sin x))))
78.0ms	(log (exp (- (/ 1.0 (sin x)) (/ (cos x) (sin x)))))
84.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify80.0ms

Counts

113 → 113

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	302	875
1	799	811
2	2888	811
3	5002	811
done	5002	811

prune257.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 29.9b

bsearch62.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	22.544919195950573	0.021208263935284816
8	-1.6220908197114983	-0.002799490342594777	-0.01337953293511418

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24
done	42	24

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1569×	body	2560	valid
1.2s	2775×	body	1280	valid
455.0ms	1868×	body	640	valid
151.0ms	943×	body	320	valid
51.0ms	467×	body	160	valid
24.0ms	375×	body	80	valid
18.0ms	3×	body	5120	valid