Details

sample190.0ms

Algorithm

intervals

Results

95.0ms	102×	body	1280	valid
34.0ms	19×	body	2560	valid
30.0ms	51×	body	640	valid
10.0ms	26×	body	320	valid
6.0ms	48×	body	80	valid
3.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize48.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
2.8b	(sin (+ x eps))

rewrite58.0ms

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:

50.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series92.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (sin (+ x eps)) (sin x))
39.0ms	(sin (+ x eps))

simplify1.2s

Counts

32 → 32

Iterations

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

prune136.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite65.0ms

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:

10.0ms	(+ x (+ x eps))
32.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
22.0ms	(cos (/ (+ x (+ x eps)) 2))

series121.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ x (+ x eps))
62.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
28.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify922.0ms

Counts

53 → 53

Iterations

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

prune240.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite128.0ms

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:

18.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
36.0ms	(cos (/ (+ x (+ x eps)) 2))
33.0ms	(cos (/ (+ x (+ x eps)) 2))
40.0ms	(cos (/ (+ x (+ x eps)) 2))

series139.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
37.0ms	(cos (/ (+ x (+ x eps)) 2))
29.0ms	(cos (/ (+ x (+ x eps)) 2))
41.0ms	(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

prune321.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
20.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(cos (/ (+ x (+ x eps)) 2))
25.0ms	(cos (/ (+ x (+ x eps)) 2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
37.0ms	(cos (/ (+ x (+ x eps)) 2))
36.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.4s

Counts

48 → 48

Iterations

Iter	Nodes
done	2011
5	2011
4	1626
3	543
2	186
1	91
0	44

prune360.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes188.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 14.7b

bsearch252.0ms

Steps

Iters	Range		Point
10	1.2035886760163307e-31	1.514112904485791e-15	1.4909178493851906e-15
10	-0.005838610583870787	-4.910260011938944e-13	-7.672969354734922e-09

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.7s	3290×	body	1280	valid
1.5s	641×	body	2560	valid
1.2s	1869×	body	640	valid
709.0ms	747×	body	320	valid
184.0ms	1112×	body	80	valid
82.0ms	341×	body	160	valid