Details

sample158.0ms

Algorithm

intervals

Results

78.0ms	137×	body	1280	valid
34.0ms	26×	body	2560	valid
22.0ms	60×	body	640	valid
6.0ms	25×	body	320	valid
1.0ms	6×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize24.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.1b	(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:

49.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

series89.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

simplify729.0ms

Counts

30 → 30

Iterations

Useful iterations: done (728.0ms)

Iter	Nodes	Cost
0	65	311
1	135	299
2	339	283
3	1210	275
done	5000	273

prune164.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize40.0ms

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)))
3.2b	(sin (/ (+ (+ x eps) x) 2))

rewrite311.0ms

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:

104.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
27.0ms	(+ (+ x eps) x)
123.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
54.0ms	(sin (/ (+ (+ x eps) x) 2))

series194.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
25.0ms	(+ (+ x eps) x)
64.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify786.0ms

Counts

72 → 72

Iterations

Useful iterations: done (783.0ms)

Iter	Nodes	Cost
0	119	1098
1	284	1081
2	1056	923
done	5001	895

prune403.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
3.2b	(sin (/ (+ (+ x eps) x) 2))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 40

Calls

3 calls:

27.0ms	(+ (+ x eps) x)
129.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
70.0ms	(sin (/ (+ (+ x eps) x) 2))

series184.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (+ x eps) x)
106.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
45.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify751.0ms

Counts

49 → 49

Iterations

Useful iterations: done (749.0ms)

Iter	Nodes	Cost
0	93	689
1	235	673
2	1089	567
done	5001	545

prune295.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

3.2b	(sin (/ (+ (+ x eps) x) 2))
5.2b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
5.2b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
5.2b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 37

Calls

4 calls:

76.0ms	(sin (/ (+ (+ x eps) x) 2))
38.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
22.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
45.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sin (/ (+ (+ x eps) x) 2))
185.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
201.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
195.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

simplify659.0ms

Counts

49 → 49

Iterations

Useful iterations: done (656.0ms)

Iter	Nodes	Cost
0	66	924
1	136	918
2	315	818
3	1108	751
done	5000	721

prune369.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.4b

regimes294.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 15.1b

bsearch148.0ms

Steps

Iters	Range		Point
9	8.931192701332034e-10	0.10130402529439038	6.966025405806914e-06
5	-1.2463973062393072e-08	-4.325919977650215e-09	-1.2287993160767815e-08

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.8s	4428×	body	1280	valid
1.2s	1893×	body	640	valid
1.0s	635×	body	2560	valid
174.0ms	662×	body	320	valid
53.0ms	301×	body	160	valid
7.0ms	81×	body	80	valid