Details

sample233.0ms

Algorithm

intervals

Results

109.0ms	143×	body	1280	valid
64.0ms	57×	body	640	valid
37.0ms	24×	body	2560	valid
7.0ms	20×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize28.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
5.0b	(cos (+ x eps))

rewrite35.0ms

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:

20.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series108.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify1.6s

Counts

32 → 32

Iterations

Iter	Nodes
5	3283
4	1332
3	588
2	270
1	137
0	67

prune329.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
5.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite181.0ms

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:

85.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
21.0ms	(+ x (+ x eps))
50.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
23.0ms	(sin (/ (+ x (+ x eps)) 2))

series234.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
38.0ms	(+ x (+ x eps))
58.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
54.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify849.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2322
2	797
1	292
0	123

prune926.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
5.4b	(sin (+ x (* eps 1/2)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `sin-sum` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`insert-posit16` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 30

Calls

2 calls:

51.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
11.0ms	(sin (+ x (* eps 1/2)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
27.0ms	(sin (+ x (* eps 1/2)))

simplify2.8s

Counts

36 → 36

Iterations

Iter	Nodes
4	3815
3	1798
2	554
1	192
0	76

prune434.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
0.2b	(* (sin x) (cos (* eps 1/2)))
0.2b	(* (cos x) (sin (* eps 1/2)))
0.3b	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

55.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
21.0ms	(* (sin x) (cos (* eps 1/2)))
19.0ms	(* (cos x) (sin (* eps 1/2)))
155.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
84.0ms	(* (sin x) (cos (* eps 1/2)))
76.0ms	(* (cos x) (sin (* eps 1/2)))
187.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

simplify4.2s

Counts

86 → 86

Iterations

Iter	Nodes
3	7884
2	1804
1	444
0	161

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes241.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	20
1	20
0	14

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.7s	4450×	body	1280	valid
1.6s	617×	body	2560	valid
1.6s	1834×	body	640	valid
324.0ms	708×	body	320	valid
124.0ms	295×	body	160	valid
13.0ms	96×	body	80	valid