Details

sample443.0ms

Algorithm

intervals

Results

132.0ms	86×	body	1280	valid
123.0ms	42×	body	2560	valid
96.0ms	64×	body	640	valid
25.0ms	36×	body	320	valid
12.0ms	17×	body	160	valid
2.0ms	11×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize23.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite388.0ms

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:

368.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(- 1.0 (cos x))

series139.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(/ (- 1.0 (cos x)) (sin x))
45.0ms	(- 1.0 (cos x))

simplify6.6s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	1918
2	594
1	240
0	106

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize271.0ms

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)))
1.7b	(- 1.0 (cos x))

rewrite163.0ms

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:

36.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
59.0ms	(/ (sin x) (- 1.0 (cos x)))
45.0ms	(- 1.0 (cos x))

series561.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
78.0ms	(/ (sin x) (- 1.0 (cos x)))
403.0ms	(- 1.0 (cos x))

simplify9.9s

Counts

168 → 168

Iterations

Iter	Nodes
done	5002
2	1681
1	575
0	239

prune2.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize152.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sqrt 1) (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

246×	`times-frac`
172×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`add-cube-cbrt`
66×	`sqrt-prod`
26×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
17×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
9×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `diff-log`

Counts

3 → 219

Calls

3 calls:

41.0ms	(/ (sqrt 1) (/ (sin x) (- 1.0 (cos x))))
33.0ms	(/ (sin x) (- 1.0 (cos x)))
54.0ms	(- 1.0 (cos x))

series817.0ms

Counts

3 → 9

Calls

3 calls:

464.0ms	(/ (sqrt 1) (/ (sin x) (- 1.0 (cos x))))
128.0ms	(/ (sin x) (- 1.0 (cos x)))
217.0ms	(- 1.0 (cos x))

simplify10.1s

Counts

228 → 228

Iterations

Iter	Nodes
done	5000
2	1735
1	722
0	294

prune2.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.4b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite382.0ms

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

Counts

4 → 112

Calls

4 calls:

73.0ms	(/ (- 1.0 (cos x)) (sin x))
221.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
47.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
17.0ms	(- 1.0 (cos x))

series854.0ms

Counts

4 → 12

Calls

4 calls:

493.0ms	(/ (- 1.0 (cos x)) (sin x))
178.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
84.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
99.0ms	(- 1.0 (cos x))

simplify6.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
3	1811
2	701
1	317
0	163

prune1.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

regimes934.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch290.0ms

Steps

Iters	Range		Point
9	2.490703692944805e-05	37.746059492850215	0.023823250578374245
9	-1.440408271564231	-1.963203309137196e-05	-0.022344650167746203

simplify19.0ms

Iterations

Iter	Nodes
done	44
1	44
0	34

end0.0ms

sample34.1s

Algorithm

intervals

Results

14.9s	1604×	body	2560	valid
11.8s	2727×	body	1280	valid
5.0s	1853×	body	640	valid
1.3s	949×	body	320	valid
256.0ms	492×	body	160	valid
119.0ms	375×	body	80	valid