Details

sample171.0ms

Algorithm

intervals

Results

78.0ms	143×	body	1280	valid
51.0ms	22×	body	2560	valid
16.0ms	45×	body	640	valid
7.0ms	30×	body	320	valid
2.0ms	14×	body	160	valid
0.0ms	2×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize24.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite39.0ms

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`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

23.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series114.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(- (cos (+ x eps)) (cos x))
29.0ms	(cos (+ x eps))

simplify893.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1232
2	337
1	135
0	65

prune217.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

60.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
24.0ms	(+ x (+ x eps))
83.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
44.0ms	(sin (/ (+ x (+ x eps)) 2))

series283.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
24.0ms	(+ x (+ x eps))
102.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
50.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify994.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1135
1	288
0	118

prune464.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 4 expressions with local error:

3.0b	(sin (/ (+ x (+ x eps)) 2))
3.0b	(sin (/ (+ x (+ x eps)) 2))
3.0b	(sin (/ (+ x (+ x eps)) 2))
5.8b	(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))) (sin (/ (+ x (+ x eps)) 2))))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

24.0ms	(sin (/ (+ x (+ x eps)) 2))
26.0ms	(sin (/ (+ x (+ x eps)) 2))
45.0ms	(sin (/ (+ x (+ x eps)) 2))
177.0ms	(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))) (sin (/ (+ x (+ x eps)) 2))))

series146.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sin (/ (+ x (+ x eps)) 2))
31.0ms	(sin (/ (+ x (+ x eps)) 2))
36.0ms	(sin (/ (+ x (+ x eps)) 2))
40.0ms	(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))) (sin (/ (+ x (+ x eps)) 2))))

simplify1.2s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	1609
3	435
2	142
1	78
0	43

prune480.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

3.0b	(sin (/ (+ x (+ x eps)) 2))
3.0b	(sin (/ (+ x (+ x eps)) 2))
3.0b	(sin (/ (+ x (+ x eps)) 2))
3.2b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 31

Calls

4 calls:

44.0ms	(sin (/ (+ x (+ x eps)) 2))
44.0ms	(sin (/ (+ x (+ x eps)) 2))
47.0ms	(sin (/ (+ x (+ x eps)) 2))
47.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sin (/ (+ x (+ x eps)) 2))
52.0ms	(sin (/ (+ x (+ x eps)) 2))
57.0ms	(sin (/ (+ x (+ x eps)) 2))
175.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ (+ x (+ x eps)) 2))))

simplify1.0s

Counts

43 → 43

Iterations

Iter	Nodes
done	5000
3	1258
2	349
1	136
0	64

prune294.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.4b

regimes490.0ms

Accuracy

94.6% (0.8b remaining)

Error of 1.2b against oracle of 0.4b and baseline of 15.5b

bsearch204.0ms

Steps

Iters	Range		Point
10	2.765405219724019e-10	1875.4132169206714	9.350772251334056e-05
9	-245180560723.46045	-1212215.9807367995	-1230266.9135965805

simplify14.0ms

Iterations

Iter	Nodes
done	40
1	40
0	30

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.7s	4444×	body	1280	valid
1.1s	1858×	body	640	valid
936.0ms	655×	body	2560	valid
242.0ms	708×	body	320	valid
43.0ms	260×	body	160	valid
6.0ms	75×	body	80	valid