Details

sample190.0ms

Algorithm

intervals

Results

119.0ms	159×	body	1280	valid
27.0ms	52×	body	640	valid
21.0ms	14×	body	2560	valid
7.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize72.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
2.0b	(cos (+ x eps))

rewrite37.0ms

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:

21.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series121.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(- (cos (+ x eps)) (cos x))
35.0ms	(cos (+ x eps))

simplify2.9s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	3787
4	1424
3	658
2	282
1	137
0	67

prune181.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
2.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite238.0ms

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:

74.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
18.0ms	(+ x (+ x eps))
99.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
46.0ms	(sin (/ (+ x (+ x eps)) 2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
25.0ms	(+ x (+ x eps))
82.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
32.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5043
3	3226
2	832
1	289
0	121

prune421.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (sin (/ eps 2)))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
2.1b	(sin (+ (/ eps 2) x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

10.0ms	(* -2 (sin (/ eps 2)))
47.0ms	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
20.0ms	(sin (+ (/ eps 2) x))

series169.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* -2 (sin (/ eps 2)))
84.0ms	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
39.0ms	(sin (+ (/ eps 2) x))

simplify2.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	1988
2	641
1	242
0	100

prune315.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`sin-cos-mult` `unswap-sqr`
1×	`associate-*r/`

Counts

4 → 86

Calls

4 calls:

9.0ms	(* (cos (/ eps 2)) (sin x))
11.0ms	(* (sin (/ eps 2)) (cos x))
50.0ms	(* (* -2 (sin (/ eps 2))) (* (cos (/ eps 2)) (sin x)))
38.0ms	(* (* -2 (sin (/ eps 2))) (* (sin (/ eps 2)) (cos x)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos (/ eps 2)) (sin x))
66.0ms	(* (sin (/ eps 2)) (cos x))
134.0ms	(* (* -2 (sin (/ eps 2))) (* (cos (/ eps 2)) (sin x)))
101.0ms	(* (* -2 (sin (/ eps 2))) (* (sin (/ eps 2)) (cos x)))

simplify1.5s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1502
1	425
0	162

prune498.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.2s	4425×	body	1280	valid
1.3s	1901×	body	640	valid
1.2s	618×	body	2560	valid
280.0ms	711×	body	320	valid
70.0ms	277×	body	160	valid
9.0ms	68×	body	80	valid