Details

sample208.0ms

Algorithm

intervals

Results

123.0ms	148×	body	1280	valid
34.0ms	19×	body	2560	valid
31.0ms	60×	body	640	valid
7.0ms	19×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	2×	body	80	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: 40.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

25.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series140.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (cos (+ x eps)) (cos x))
51.0ms	(cos (+ x eps))

simplify2.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	3787
4	1424
3	658
2	282
1	137
0	67

prune177.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite185.0ms

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-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

29.0ms	(+ x (+ x eps))
127.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
28.0ms	(sin (/ (+ x (+ x eps)) 2))

series150.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ x (+ x eps))
74.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.7s

Counts

53 → 53

Iterations

Iter	Nodes
done	5016
3	2226
2	589
1	214
0	92

prune302.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.0b	(sin (/ (+ x (+ x eps)) 2))
3.0b	(sin (/ (+ x (+ x eps)) 2))
3.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite138.0ms

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:

14.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
41.0ms	(sin (/ (+ x (+ x eps)) 2))
34.0ms	(sin (/ (+ x (+ x eps)) 2))
47.0ms	(sin (/ (+ x (+ x eps)) 2))

series293.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
56.0ms	(sin (/ (+ x (+ x eps)) 2))
47.0ms	(sin (/ (+ x (+ x eps)) 2))
54.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
4	2826
3	747
2	260
1	123
0	59

prune381.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (* 1/2 eps)))
0.6b	(cbrt (sin (* 1/2 eps)))
0.6b	(cbrt (sin (* 1/2 eps)))
3.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

7.0ms	(cbrt (sin (* 1/2 eps)))
3.0ms	(cbrt (sin (* 1/2 eps)))
3.0ms	(cbrt (sin (* 1/2 eps)))
36.0ms	(sin (/ (+ x (+ x eps)) 2))

series548.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (sin (* 1/2 eps)))
190.0ms	(cbrt (sin (* 1/2 eps)))
171.0ms	(cbrt (sin (* 1/2 eps)))
53.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.8s

Counts

56 → 56

Iterations

Iter	Nodes
done	5002
4	2281
3	698
2	252
1	125
0	60

prune324.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.3b

regimes269.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.5b

bsearch237.0ms

Steps

Iters	Range		Point
8	0.113095154289168	29.100869698027953	0.11407284983207572
10	-1.4244285555183042e-05	-9.550132857780223e-23	-4.028105222915818e-06

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.6s	4454×	body	1280	valid
1.3s	658×	body	2560	valid
1.3s	1824×	body	640	valid
288.0ms	696×	body	320	valid
60.0ms	286×	body	160	valid
9.0ms	82×	body	80	valid