Details

sample172.0ms

Algorithm

intervals

Results

71.0ms	98×	body	1280	valid
33.0ms	24×	body	2560	valid
25.0ms	56×	body	640	valid
7.0ms	22×	body	320	valid
4.0ms	44×	body	80	valid
3.0ms	12×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize19.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.7b	(sin (+ x eps))

rewrite103.0ms

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:

83.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

series109.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (sin (+ x eps)) (sin x))
36.0ms	(sin (+ x eps))

simplify7.2s

Counts

32 → 32

Iterations

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

prune466.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize78.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2))))
0.0b	(+ x (+ eps x))
0.2b	(* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2)))
2.8b	(cos (/ (+ x (+ eps x)) 2))

rewrite252.0ms

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-cos-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

112.0ms	(* 2 (* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2))))
41.0ms	(+ x (+ eps x))
29.0ms	(* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2)))
66.0ms	(cos (/ (+ x (+ eps x)) 2))

series344.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* 2 (* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2))))
42.0ms	(+ x (+ eps x))
128.0ms	(* (sin (* eps 1/2)) (cos (/ (+ x (+ eps x)) 2)))
45.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify5.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	3562
2	866
1	301
0	122

prune829.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* 2 (sin (* 1/2 eps))) (cos (+ x (* 1/2 eps))))
2.8b	(cos (+ x (* 1/2 eps)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

56.0ms	(* (* 2 (sin (* 1/2 eps))) (cos (+ x (* 1/2 eps))))
13.0ms	(cos (+ x (* 1/2 eps)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(* (* 2 (sin (* 1/2 eps))) (cos (+ x (* 1/2 eps))))
32.0ms	(cos (+ x (* 1/2 eps)))

simplify3.8s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	2256
2	543
1	173
0	68

prune320.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite281.0ms

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` `cos-mult` `cbrt-unprod` `sin-mult`
4×	`associate-*r/` `insert-posit16`
3×	`sub-neg` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`diff-log`

Counts

4 → 82

Calls

4 calls:

23.0ms	(* (cos x) (cos (* 1/2 eps)))
48.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
26.0ms	(* (sin x) (sin (* 1/2 eps)))
181.0ms	(* (* 2 (sin (* 1/2 eps))) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))

series536.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos x) (cos (* 1/2 eps)))
152.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
83.0ms	(* (sin x) (sin (* 1/2 eps)))
227.0ms	(* (* 2 (sin (* 1/2 eps))) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))

simplify2.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	1362
1	397
0	150

prune788.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes416.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	42
3	42
2	35
1	29
0	16

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.7s	3263×	body	1280	valid
774.0ms	649×	body	2560	valid
621.0ms	1897×	body	640	valid
183.0ms	762×	body	320	valid
71.0ms	1093×	body	80	valid
46.0ms	336×	body	160	valid