Details

sample56.0ms

Algorithm

intervals

Results

29.0ms	60×	body	2560	valid
9.0ms	41×	body	1280	valid
5.0ms	36×	body	640	valid
3.0ms	26×	body	320	valid
2.0ms	84×	body	80	valid
1.0ms	9×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4
done	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize6.0ms

Local error

Found 2 expressions with local error:

1.0b	(- 1.0 (cos x))
17.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
18.0ms	(/ (- 1.0 (cos x)) (* x x))

series69.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
50.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239
done	5002	239

prune107.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
1.0b	(- 1.0 (cos x))
1.0b	(- 1.0 (cos x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
40×	`sqrt-prod`
38×	`add-cube-cbrt`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
4×	`pow1` `flip3--` `sqrt-div` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

17.0ms	(/ (sqrt (- 1.0 (cos x))) x)
15.0ms	(/ (sqrt (- 1.0 (cos x))) x)
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series224.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (sqrt (- 1.0 (cos x))) x)
92.0ms	(/ (sqrt (- 1.0 (cos x))) x)
19.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify97.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	242	1020
1	706	972
2	2968	960
3	5002	960
done	5002	960

prune307.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))
1.0b	(- 1.0 (cos x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
10×	`add-log-exp`
9×	`sqr-pow`
7×	`add-cube-cbrt`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sqr-cos` `associate-+l+` `distribute-rgt-out` `pow-pow` `flip3-+` `unpow3` `pow-exp` `sum-log` `flip-+` `rem-cube-cbrt`

Counts

4 → 84

Calls

4 calls:

6.0ms	(pow (cos x) 3)
12.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
23.0ms	(- (pow 1.0 3) (pow (cos x) 3))
6.0ms	(- 1.0 (cos x))

series140.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos x) 3)
45.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))
20.0ms	(- 1.0 (cos x))

simplify60.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	361	583
1	1558	544
2	5003	524
done	5003	524

prune334.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.9b	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
0.9b	(log (exp (pow (cos x) 3)))
1.0b	(- 1.0 (cos x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `log-pow`
12×	`exp-prod`
9×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `log-prod`
5×	`difference-of-squares`
4×	`add-exp-log` `unpow-prod-down` `cube-prod` `add-cbrt-cube`
3×	`associate--r+` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `sqr-pow`
1×	`+-commutative` `cube-mult` `sqr-cos` `associate-+l+` `distribute-rgt-out` `flip3-+` `unpow3` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 72

Calls

4 calls:

12.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
39.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
7.0ms	(log (exp (pow (cos x) 3)))
6.0ms	(- 1.0 (cos x))

series143.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
53.0ms	(- (pow 1.0 3) (log (exp (pow (cos x) 3))))
29.0ms	(log (exp (pow (cos x) 3)))
20.0ms	(- 1.0 (cos x))

simplify41.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	357	517
1	1269	431
2	5001	426
done	5001	426

prune339.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes81.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.6b

bsearch93.0ms

Steps

Iters	Range		Point
10	4.250299402880914e-15	0.02319676823116778	0.022874134562334194
7	-0.15939393977811658	-0.001391736753177052	-0.0295890883960637

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	57
1	61	57
done	61	57

end0.0ms

sample1.5s

Algorithm

intervals

Results

708.0ms	1569×	body	2560	valid
263.0ms	1230×	body	1280	valid
212.0ms	1551×	body	640	valid
87.0ms	907×	body	320	valid
77.0ms	2307×	body	80	valid
29.0ms	436×	body	160	valid