Details

sample95.0ms

Algorithm

intervals

Results

45.0ms	113×	body	1280	valid
17.0ms	60×	body	640	valid
16.0ms	18×	body	2560	valid
4.0ms	23×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify140.0ms

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164
done	5001	164

prune77.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
3.3b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

14.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
11.0ms	(* (cos x) (sin eps))
49.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series291.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (cos eps))
47.0ms	(* (cos x) (sin eps))
111.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify39.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543
done	5001	543

prune218.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
2.2b	(- (cos eps) 1)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

21.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
28.0ms	(* (sin x) (- (cos eps) 1))
11.0ms	(* (cos x) (sin eps))
7.0ms	(- (cos eps) 1)

series232.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
47.0ms	(* (sin x) (- (cos eps) 1))
46.0ms	(* (cos x) (sin eps))
20.0ms	(- (cos eps) 1)

simplify42.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499
done	5001	499

prune252.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.3b	(* (cos eps) (cos eps))
0.4b	(+ (cos eps) 1)
2.2b	(- (* (cos eps) (cos eps)) 1)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`pow1` `*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-r` `associate-l`
3×	`swap-sqr`
2×	`sqr-cos` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `pow2` `sub-neg` `flip3--` `flip3-+` `pow-plus` `diff-log` `difference-of-sqr-1` `associate--l+` `sum-log` `sub-1-cos` `pow-sqr` `cos-mult` `pow-prod-up` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

11.0ms	(* (cos x) (sin eps))
12.0ms	(* (cos eps) (cos eps))
6.0ms	(+ (cos eps) 1)
11.0ms	(- (* (cos eps) (cos eps)) 1)

series106.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos x) (sin eps))
19.0ms	(* (cos eps) (cos eps))
10.0ms	(+ (cos eps) 1)
32.0ms	(- (* (cos eps) (cos eps)) 1)

simplify42.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	310	375
1	1267	322
2	5001	317
done	5001	317

prune236.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes103.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	31	13
2	32	13
3	32	13
done	32	13

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3326×	body	1280	valid
606.0ms	673×	body	2560	valid
460.0ms	1887×	body	640	valid
110.0ms	706×	body	320	valid
53.0ms	1078×	body	80	valid
35.0ms	330×	body	160	valid