Details

sample181.0ms

Algorithm

intervals

Results

89.0ms	115×	body	1280	valid
28.0ms	28×	body	320	valid
26.0ms	50×	body	640	valid
19.0ms	14×	body	2560	valid
4.0ms	34×	body	80	valid
3.0ms	15×	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: 36.5b

localize13.0ms

Local error

Found 2 expressions with local error:

1.8b	(sin (+ x eps))
2.0b	(- (sin (+ x eps)) (sin x))

rewrite84.0ms

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:

17.0ms	(sin (+ x eps))
67.0ms	(- (sin (+ x eps)) (sin x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sin (+ x eps))
75.0ms	(- (sin (+ x eps)) (sin x))

simplify3.5s

Counts

32 → 32

Iterations

Iter	Nodes
done	5016
5	4587
4	1727
3	752
2	305
1	136
0	65

prune133.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ eps x))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2)))
2.1b	(cos (/ (+ x (+ eps x)) 2))

rewrite64.0ms

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-+` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

16.0ms	(+ x (+ eps x))
19.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2)))
29.0ms	(cos (/ (+ x (+ eps x)) 2))

series152.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ x (+ eps x))
91.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2)))
31.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.7s

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
3	2448
2	603
1	211
0	89

prune349.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))

rewrite102.0ms

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` `pow1/3`

Counts

4 → 34

Calls

4 calls:

10.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
32.0ms	(cos (/ (+ x (+ eps x)) 2))
36.0ms	(cos (/ (+ x (+ eps x)) 2))
23.0ms	(cos (/ (+ x (+ eps x)) 2))

series227.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
28.0ms	(cos (/ (+ x (+ eps x)) 2))
33.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.9s

Counts

46 → 46

Iterations

Iter	Nodes
done	5002
4	2854
3	799
2	246
1	132
0	64

prune397.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize67.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))
2.1b	(cos (/ (+ x (+ eps x)) 2))

rewrite97.0ms

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` `pow1/3`

Counts

4 → 34

Calls

4 calls:

8.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
32.0ms	(cos (/ (+ x (+ eps x)) 2))
22.0ms	(cos (/ (+ x (+ eps x)) 2))
34.0ms	(cos (/ (+ x (+ eps x)) 2))

series249.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (* (cos (/ (+ x (+ eps x)) 2)) (sin (* eps 1/2))))
25.0ms	(cos (/ (+ x (+ eps x)) 2))
33.0ms	(cos (/ (+ x (+ eps x)) 2))
35.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.5s

Counts

46 → 46

Iterations

Iter	Nodes
done	5002
4	2854
3	799
2	246
1	132
0	64

prune354.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.6b

regimes150.0ms

Accuracy

98.3% (0.3b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.3b

bsearch149.0ms

Steps

Iters	Range		Point
8	6.0329627772416755e-24	1.9249297628844816e-20	1.8942327691411048e-20
9	-5.984165099293203e-09	-2.0017119239229129e-16	-5.893930927518443e-09

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.9s	3310×	body	1280	valid
817.0ms	1858×	body	640	valid
744.0ms	618×	body	2560	valid
242.0ms	764×	body	320	valid
83.0ms	1111×	body	80	valid
81.0ms	339×	body	160	valid