Details

sample242.0ms

Algorithm

intervals

Results

127.0ms	116×	body	1280	valid
48.0ms	27×	body	2560	valid
36.0ms	54×	body	640	valid
9.0ms	19×	body	320	valid
5.0ms	33×	body	80	valid
2.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize39.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sin (+ x eps)) (sin x))
2.6b	(sin (+ x eps))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

49.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

series82.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify1.7s

Counts

32 → 32

Iterations

Iter	Nodes
5	3374
4	1441
3	637
2	294
1	137
0	65

prune396.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

23.0ms	(+ x (+ x eps))
33.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
47.0ms	(cos (/ (+ x (+ x eps)) 2))

series168.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ x (+ x eps))
86.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify5.1s

Counts

53 → 53

Iterations

Iter	Nodes
4	7454
3	1757
2	596
1	221
0	94

prune594.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
27.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))

series212.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
24.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.4s

Counts

48 → 48

Iterations

Iter	Nodes
6	2069
5	1011
4	589
3	314
2	157
1	89
0	44

prune736.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`rem-log-exp`

Counts

4 → 40

Calls

4 calls:

60.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
44.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

series160.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.1s

Counts

52 → 52

Iterations

Iter	Nodes
8	2922
7	1160
6	673
5	424
4	297
3	204
2	126
1	88
0	49

prune910.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes200.0ms

Accuracy

99% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.9b

bsearch299.0ms

Steps

Iters	Range		Point
9	6.506845775939919e-17	2.0554446490307063e-08	1.300741008615541e-08
10	-8.26555774309129e+15	-0.09702975014721212	-0.0987473663124097

simplify13.0ms

Iterations

Iter	Nodes
2	35
1	35
0	25

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.5s	3225×	body	1280	valid
1.8s	1858×	body	640	valid
1.3s	695×	body	2560	valid
333.0ms	769×	body	320	valid
195.0ms	1102×	body	80	valid
169.0ms	351×	body	160	valid