Details

sample90.0ms

Algorithm

intervals

Results

34.0ms	87×	body	1280	valid
21.0ms	24×	body	2560	valid
17.0ms	77×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	30×	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: 35.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ x eps))

rewrite55.0ms

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:

44.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series66.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify136.0ms

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

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.6b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 66

Calls

4 calls:

13.0ms	(- (* (cos x) (sin eps)) (sin x))
11.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (cos eps))
31.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* (cos x) (sin eps)) (sin x))
45.0ms	(* (cos x) (sin eps))
50.0ms	(* (sin x) (cos eps))
117.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify41.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565
done	5002	565

prune227.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (- (cos eps) 1))
2.7b	(- (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)))
14.0ms	(* (cos x) (sin eps))
26.0ms	(* (sin x) (- (cos eps) 1))
7.0ms	(- (cos eps) 1)

series235.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
44.0ms	(* (cos x) (sin eps))
52.0ms	(* (sin x) (- (cos eps) 1))
19.0ms	(- (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

prune246.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.7b	(+ (* (sin x) (cos eps)) (- (sin x)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`sum-log`
6×	`associate-r` `associate-l`
3×	`associate-+l-`
2×	`+-commutative` `neg-sub0` `associate-+r-` `flip3-+` `unsub-neg` `pow-prod-down` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`associate-+l+` `sin-cos-mult`

Counts

4 → 69

Calls

4 calls:

65.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (cos eps))
14.0ms	(+ (* (sin x) (cos eps)) (- (sin x)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
45.0ms	(* (cos x) (sin eps))
49.0ms	(* (sin x) (cos eps))
59.0ms	(+ (* (sin x) (cos eps)) (- (sin x)))

simplify42.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	339	587
1	1426	530
2	5001	517
done	5001	517

prune201.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10
done	18	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3355×	body	1280	valid
587.0ms	646×	body	2560	valid
441.0ms	1810×	body	640	valid
126.0ms	747×	body	320	valid
59.0ms	1099×	body	80	valid
35.0ms	343×	body	160	valid