Details

sample196.0ms

Algorithm

intervals

Results

112.0ms	145×	body	1280	valid
30.0ms	22×	body	2560	valid
29.0ms	55×	body	640	valid
11.0ms	26×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize61.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite31.0ms

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:

18.0ms	(- (cos (+ x eps)) (cos x))
13.0ms	(cos (+ x eps))

series125.0ms

Counts

2 → 6

Calls

2 calls:

104.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

simplify849.0ms

Counts

32 → 32

Iterations

Iter	Nodes
done	2008
4	1424
3	658
2	282
1	137
0	67

prune156.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x eps))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
2.4b	(sin (/ (+ x (+ x eps)) 2))

rewrite152.0ms

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:

10.0ms	(+ x (+ x eps))
64.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
55.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
22.0ms	(sin (/ (+ x (+ x eps)) 2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ x (+ x eps))
87.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
71.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
50.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify508.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2000
2	852
1	291
0	123

prune378.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
2.4b	(sin (/ (+ x (+ x eps)) 2))

rewrite127.0ms

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:

20.0ms	(+ x (+ x eps))
67.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
39.0ms	(sin (/ (+ x (+ x eps)) 2))

series146.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ x (+ x eps))
78.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ x (+ x eps)) 2)))
41.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify566.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	2000
2	743
1	241
0	96

prune290.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
2.4b	(sin (/ (+ x (+ x eps)) 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt (sin (/ eps 2)))
1.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

series472.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (sin (/ eps 2)))
166.0ms	(cbrt (sin (/ eps 2)))
118.0ms	(cbrt (sin (/ eps 2)))
41.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify566.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
3	648
2	234
1	125
0	62

prune347.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.3b

regimes249.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.7b

bsearch290.0ms

Steps

Iters	Range		Point
10	0.0038666078177206752	941504501108.8118	0.00391800888554098
10	-121993772661.31783	-0.22068356154967622	-0.22306452923435388

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	26

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.6s	4457×	body	1280	valid
1.8s	665×	body	2560	valid
1.3s	1832×	body	640	valid
393.0ms	668×	body	320	valid
83.0ms	298×	body	160	valid
10.0ms	80×	body	80	valid