Details

sample251.0ms

Algorithm

intervals

Results

144.0ms	151×	body	1280	valid
48.0ms	27×	body	2560	valid
35.0ms	54×	body	640	valid
8.0ms	17×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	1×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize25.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (cos (+ x eps)) (cos x))
2.7b	(cos (+ x eps))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

23.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

series88.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify1.6s

Counts

32 → 32

Iterations

Iter	Nodes
5	3258
4	1330
3	586
2	268
1	135
0	67

prune373.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.4b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
2.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

58.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
14.0ms	(+ x (+ x eps))
58.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
30.0ms	(+ x (+ x eps))
64.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
40.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify942.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2396
2	826
1	289
0	123

prune924.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.4b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
2.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`sum-log` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 43

Calls

3 calls:

13.0ms	(+ x (+ x eps))
82.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
23.0ms	(sin (/ (+ x (+ x eps)) 2))

series165.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ x (+ x eps))
72.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
48.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

52 → 52

Iterations

Iter	Nodes
3	2381
2	732
1	239
0	96

prune570.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.5b

localize76.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
2.9b	(sin (/ (+ x (+ x eps)) 2))
2.9b	(sin (/ (+ x (+ x eps)) 2))
2.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite133.0ms

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:

10.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
34.0ms	(sin (/ (+ x (+ x eps)) 2))
46.0ms	(sin (/ (+ x (+ x eps)) 2))
42.0ms	(sin (/ (+ x (+ x eps)) 2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))
45.0ms	(sin (/ (+ x (+ x eps)) 2))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.3s

Counts

48 → 48

Iterations

Iter	Nodes
5	4346
4	1461
3	536
2	249
1	121
0	59

prune716.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.5b

regimes316.0ms

Accuracy

97% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 14.9b

bsearch235.0ms

Steps

Iters	Range		Point
9	6.506845775939919e-17	2.0554446490307063e-08	2.0143977468052977e-08
10	-8.26555774309129e+15	-0.09702975014721212	-0.0987473663124097

simplify10.0ms

Iterations

Iter	Nodes
2	35
1	35
0	26

end0.0ms

sample8.7s

Algorithm

intervals

Results

5.4s	4397×	body	1280	valid
1.6s	695×	body	2560	valid
1.2s	1915×	body	640	valid
278.0ms	655×	body	320	valid
69.0ms	266×	body	160	valid
9.0ms	72×	body	80	valid