Details

sample256.0ms

Algorithm

intervals

Results

166.0ms	153×	body	1280	valid
36.0ms	20×	body	2560	valid
34.0ms	54×	body	640	valid
5.0ms	14×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	5×	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: 38.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite29.0ms

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:

16.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series99.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (cos (+ x eps)) (cos x))
35.0ms	(cos (+ x eps))

simplify1.1s

Counts

32 → 32

Iterations

Iter	Nodes
done	2044
5	2044
4	1424
3	658
2	282
1	137
0	67

prune181.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize48.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
2.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite131.0ms

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:

12.0ms	(+ x (+ x eps))
74.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
45.0ms	(sin (/ (+ x (+ x eps)) 2))

series162.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ x (+ x eps))
80.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
49.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.0s

Counts

53 → 53

Iterations

Iter	Nodes
done	2006
3	2006
2	590
1	216
0	94

prune357.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
2.9b	(sin (/ (+ x (+ x eps)) 2))
2.9b	(sin (/ (+ x (+ x eps)) 2))
2.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite111.0ms

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:

18.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))
35.0ms	(sin (/ (+ x (+ x eps)) 2))
20.0ms	(sin (/ (+ x (+ x eps)) 2))

series331.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
54.0ms	(sin (/ (+ x (+ x eps)) 2))
55.0ms	(sin (/ (+ x (+ x eps)) 2))
56.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	2009
4	2009
3	747
2	260
1	123
0	59

prune381.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
2.9b	(sin (/ (+ x (+ x eps)) 2))
2.9b	(sin (/ (+ x (+ x eps)) 2))
2.9b	(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:

17.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
43.0ms	(sin (/ (+ x (+ x eps)) 2))
39.0ms	(sin (/ (+ x (+ x eps)) 2))
39.0ms	(sin (/ (+ x (+ x eps)) 2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))
46.0ms	(sin (/ (+ x (+ x eps)) 2))
50.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	2009
4	2009
3	747
2	260
1	123
0	59

prune306.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.4b

regimes399.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch296.0ms

Steps

Iters	Range		Point
10	5.037382729650074e-10	232.09055164250086	2.2247927857601395e-06
10	-1.3816842601692823e-07	-2.482857645479789e-25	-1.347365952010613e-07

simplify7.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.7s	4455×	body	1280	valid
1.5s	656×	body	2560	valid
1.1s	1802×	body	640	valid
741.0ms	719×	body	320	valid
72.0ms	287×	body	160	valid
10.0ms	81×	body	80	valid