Details

sample225.0ms

Algorithm

intervals

Results

88.0ms	104×	body	1280	valid
66.0ms	21×	body	2560	valid
27.0ms	51×	body	640	valid
10.0ms	28×	body	320	valid
4.0ms	36×	body	80	valid
4.0ms	16×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize62.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ x eps))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

110.0ms	(- (sin (+ x eps)) (sin x))
41.0ms	(sin (+ x eps))

series121.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (sin (+ x eps)) (sin x))
34.0ms	(sin (+ x eps))

simplify8.6s

Counts

32 → 32

Iterations

Iter	Nodes
done	5004
5	4830
4	1837
3	761
2	306
1	136
0	65

prune368.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize109.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ eps x))
0.2b	(/ (+ x (+ eps x)) 2)
0.2b	(* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2)))
3.6b	(cos (/ (+ x (+ eps x)) 2))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-cos-mult` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

65.0ms	(+ x (+ eps x))
159.0ms	(/ (+ x (+ eps x)) 2)
66.0ms	(* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2)))
60.0ms	(cos (/ (+ x (+ eps x)) 2))

series263.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ x (+ eps x))
50.0ms	(/ (+ x (+ eps x)) 2)
111.0ms	(* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2)))
55.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify6.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5002
3	3133
2	894
1	310
0	137

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize90.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (+ x (/ eps 2))) (sin (/ eps 2)))
3.6b	(cos (+ x (/ eps 2)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

47.0ms	(* (cos (+ x (/ eps 2))) (sin (/ eps 2)))
56.0ms	(cos (+ x (/ eps 2)))

series220.0ms

Counts

2 → 6

Calls

2 calls:

173.0ms	(* (cos (+ x (/ eps 2))) (sin (/ eps 2)))
47.0ms	(cos (+ x (/ eps 2)))

simplify4.9s

Counts

34 → 34

Iterations

Iter	Nodes
done	5001
4	2213
3	866
2	307
1	136
0	64

prune492.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

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

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`associate-*l/` `insert-posit16`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log`

Counts

4 → 78

Calls

4 calls:

32.0ms	(* (cos x) (cos (/ eps 2)))
35.0ms	(- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2))))
54.0ms	(* (sin x) (sin (/ eps 2)))
128.0ms	(* (- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2)))) (sin (/ eps 2)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cos x) (cos (/ eps 2)))
173.0ms	(- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2))))
101.0ms	(* (sin x) (sin (/ eps 2)))
284.0ms	(* (- (* (cos x) (cos (/ eps 2))) (* (sin x) (sin (/ eps 2)))) (sin (/ eps 2)))

simplify5.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
3	3424
2	930
1	336
0	143

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes487.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.2s	3236×	body	1280	valid
1.0s	1918×	body	640	valid
816.0ms	617×	body	2560	valid
254.0ms	766×	body	320	valid
101.0ms	1090×	body	80	valid
71.0ms	373×	body	160	valid