Details

sample211.0ms

Algorithm

intervals

Results

91.0ms	47×	body	2560	valid
65.0ms	92×	body	1280	valid
24.0ms	65×	body	640	valid
7.0ms	28×	body	320	valid
5.0ms	1×	body	5120	valid
3.0ms	15×	body	160	valid
1.0ms	8×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite50.0ms

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

Counts

2 → 52

Calls

2 calls:

44.0ms	(/ (- 1.0 (cos x)) (sin x))
5.0ms	(- 1.0 (cos x))

series81.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify819.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune362.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
5.0ms	(- 1.0 (cos x))

series91.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify538.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune253.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
3×	`log-prod` `associate-/r*` `div-sub` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
16.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
30.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
9.0ms	(- 1.0 (cos x))

series184.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
62.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
49.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
31.0ms	(- 1.0 (cos x))

simplify527.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	962
1	318
0	163

prune747.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.4b	(* (/ 1 (sin x)) (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-l`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`associate-/r` `sub-neg` `flip3--` `flip--` `associate-/l` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `rec-exp` `distribute-lft-in` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`clear-num` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 90

Calls

3 calls:

10.0ms	(/ 1 (sin x))
50.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
9.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ 1 (sin x))
56.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
31.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5004
2	2400
1	380
0	150

prune292.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes330.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.8b

bsearch119.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.018056437645311372
7	-0.10952899301968014	-0.00181011214377754	-0.022988205514711212

simplify10.0ms

Iterations

Iter	Nodes
done	44
2	44
1	42
0	29

end0.0ms

sample9.1s

Algorithm

intervals

Results

3.8s	1672×	body	2560	valid
3.4s	2688×	body	1280	valid
949.0ms	1889×	body	640	valid
418.0ms	898×	body	320	valid
136.0ms	499×	body	160	valid
42.0ms	351×	body	80	valid
14.0ms	3×	body	5120	valid