Details

sample157.0ms

Algorithm

intervals

Results

91.0ms	137×	body	1280	valid
22.0ms	63×	body	640	valid
21.0ms	17×	body	2560	valid
7.0ms	29×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

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

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

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:

29.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

series119.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (cos (+ x eps)) (cos x))
30.0ms	(cos (+ x eps))

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (471.0ms)

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

prune101.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

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))

rewrite366.0ms

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:

116.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
39.0ms	(+ (+ x eps) x)
150.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
60.0ms	(sin (/ (+ (+ x eps) x) 2))

series283.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
31.0ms	(+ (+ x eps) x)
106.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
49.0ms	(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

prune266.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

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))

rewrite244.0ms

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:

30.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
66.0ms	(sin (/ (+ (+ x eps) x) 2))
57.0ms	(sin (/ (+ (+ x eps) x) 2))
90.0ms	(sin (/ (+ (+ x eps) x) 2))

series303.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
54.0ms	(sin (/ (+ (+ x eps) x) 2))
50.0ms	(sin (/ (+ (+ x eps) x) 2))
36.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.8s

Counts

44 → 44

Iterations

Useful iterations: 4 (534.0ms)

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

prune237.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

localize39.0ms

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))

rewrite157.0ms

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:

18.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
44.0ms	(sin (/ (+ (+ x eps) x) 2))
47.0ms	(sin (/ (+ (+ x eps) x) 2))
47.0ms	(sin (/ (+ (+ x eps) x) 2))

series226.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
36.0ms	(sin (/ (+ (+ x eps) x) 2))
37.0ms	(sin (/ (+ (+ x eps) x) 2))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.7s

Counts

44 → 44

Iterations

Useful iterations: 4 (384.0ms)

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

prune254.0ms

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

bsearch169.0ms

Steps

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

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.3s	4513×	body	1280	valid
975.0ms	598×	body	2560	valid
834.0ms	1834×	body	640	valid
247.0ms	703×	body	320	valid
48.0ms	269×	body	160	valid
8.0ms	83×	body	80	valid