Details

sample129.0ms

Algorithm

intervals

Results

68.0ms	137×	body	1280	valid
21.0ms	63×	body	640	valid
18.0ms	17×	body	2560	valid
7.0ms	29×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	2×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.0b	(cos (+ x eps))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

58.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series91.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (489.0ms)

Iter	Nodes	Cost
0	65	311
1	135	299
2	266	283
3	540	275
4	1076	273
5	2577	273
done	5001	273

prune90.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
4.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite404.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
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-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

141.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
57.0ms	(+ (+ x eps) x)
129.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
72.0ms	(sin (/ (+ (+ x eps) x) 2))

series279.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
29.0ms	(+ (+ x eps) x)
93.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
35.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.4s

Counts

72 → 72

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	119	1098
1	277	1081
2	810	919
3	2388	895
done	5000	889

prune270.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
4.0b	(sin (/ (+ (+ x eps) x) 2))
4.0b	(sin (/ (+ (+ x eps) x) 2))
4.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

36.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
86.0ms	(sin (/ (+ (+ x eps) x) 2))
90.0ms	(sin (/ (+ (+ x eps) x) 2))
77.0ms	(sin (/ (+ (+ x eps) x) 2))

series292.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))
54.0ms	(sin (/ (+ (+ x eps) x) 2))
52.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.7s

Counts

44 → 44

Iterations

Useful iterations: 4 (512.0ms)

Iter	Nodes	Cost
0	57	570
1	120	567
2	251	501
3	519	477
4	1308	467
5	3961	467
done	5000	467

prune257.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
4.0b	(sin (/ (+ (+ x eps) x) 2))
4.0b	(sin (/ (+ (+ x eps) x) 2))
4.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

31.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
65.0ms	(sin (/ (+ (+ x eps) x) 2))
82.0ms	(sin (/ (+ (+ x eps) x) 2))
75.0ms	(sin (/ (+ (+ x eps) x) 2))

series251.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
36.0ms	(sin (/ (+ (+ x eps) x) 2))
32.0ms	(sin (/ (+ (+ x eps) x) 2))
38.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.8s

Counts

44 → 44

Iterations

Useful iterations: 4 (518.0ms)

Iter	Nodes	Cost
0	57	570
1	120	567
2	251	501
3	519	477
4	1308	467
5	3961	467
done	5000	467

prune251.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.2b

regimes179.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.0b

bsearch215.0ms

Steps

Iters	Range		Point
11	8.666561730544872e-18	9556.682540875734	4.781000628187973e-06
7	-0.006495210018506858	-9.497075983896804e-05	-0.0006111174932312063

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	51
1	35	51
done	35	51

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.3s	4513×	body	1280	valid
1.3s	598×	body	2560	valid
1.0s	1834×	body	640	valid
188.0ms	703×	body	320	valid
50.0ms	269×	body	160	valid
8.0ms	83×	body	80	valid