Details

sample191.0ms

Algorithm

intervals

Results

117.0ms	120×	body	1280	valid
24.0ms	59×	body	640	valid
24.0ms	20×	body	2560	valid
4.0ms	13×	body	320	valid
3.0ms	31×	body	80	valid
3.0ms	13×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize27.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
2.8b	(sin (+ x eps))

rewrite81.0ms

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:

66.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series85.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify1.3s

Counts

32 → 32

Iterations

Iter	Nodes
done	2009
5	2009
4	1723
3	751
2	308
1	137
0	65

prune349.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

22.0ms	(+ x (+ x eps))
26.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
34.0ms	(cos (/ (+ x (+ x eps)) 2))

series145.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ x (+ x eps))
71.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify949.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	2005
3	2005
2	654
1	221
0	92

prune674.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 36

Calls

4 calls:

21.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
21.0ms	(cos (/ (+ x (+ x eps)) 2))
24.0ms	(cos (/ (+ x (+ x eps)) 2))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

series156.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
41.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	2019
5	2019
4	1195
3	396
2	139
1	83
0	45

prune683.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))
3.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `cos-mult`

Counts

4 → 35

Calls

4 calls:

6.0ms	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))))
41.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))
24.0ms	(cos (/ (+ x (+ x eps)) 2))

series225.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))))
32.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
43.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.5s

Counts

47 → 47

Iterations

Iter	Nodes
done	2000
5	2000
4	1742
3	571
2	190
1	105
0	50

prune675.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.5b

regimes282.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.0b

bsearch257.0ms

Steps

Iters	Range		Point
10	5.037382729650074e-10	232.09055164250086	1.1933581741857647e-08
10	-1.3816842601692823e-07	-2.482857645479789e-25	-1.7789715079372338e-08

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.6s	3303×	body	1280	valid
2.0s	656×	body	2560	valid
1.1s	1817×	body	640	valid
419.0ms	779×	body	320	valid
127.0ms	1081×	body	80	valid
92.0ms	364×	body	160	valid