Details

sample289.0ms

Algorithm

intervals

Results

129.0ms	129×	body	1280	valid
89.0ms	29×	body	2560	valid
41.0ms	62×	body	640	valid
13.0ms	28×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize29.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
4.1b	(cos (+ x eps))

rewrite20.0ms

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:

11.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series98.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify1.6s

Counts

32 → 32

Iterations

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

prune203.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
4.2b	(sin (/ (+ x (+ x eps)) 2))

rewrite203.0ms

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:

70.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
22.0ms	(+ x (+ x eps))
73.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
36.0ms	(sin (/ (+ x (+ x eps)) 2))

series239.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
43.0ms	(+ x (+ x eps))
67.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
3	2396
2	826
1	289
0	123

prune419.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
4.2b	(sin (+ x (* eps 1/2)))

rewrite70.0ms

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:

59.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
10.0ms	(sin (+ x (* eps 1/2)))

series110.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
38.0ms	(sin (+ x (* eps 1/2)))

simplify3.4s

Counts

36 → 36

Iterations

Iter	Nodes
4	4094
3	1842
2	563
1	190
0	76

prune218.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

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:

38.0ms	(* (cos x) (sin (* eps 1/2)))
19.0ms	(* (sin x) (cos (* eps 1/2)))
29.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
94.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (cos x) (sin (* eps 1/2)))
67.0ms	(* (sin x) (cos (* eps 1/2)))
107.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
201.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

simplify10.7s

Counts

86 → 86

Iterations

Iter	Nodes
3	8631
2	1885
1	442
0	161

prune533.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes241.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	22
1	22
0	15

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.5s	4377×	body	1280	valid
1.6s	1903×	body	640	valid
1.2s	640×	body	2560	valid
268.0ms	714×	body	320	valid
69.0ms	280×	body	160	valid
10.0ms	86×	body	80	valid