Details

sample186.0ms

Algorithm

intervals

Results

115.0ms	143×	body	1280	valid
24.0ms	62×	body	640	valid
20.0ms	14×	body	2560	valid
7.0ms	22×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	3×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize15.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite27.0ms

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:

16.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series117.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (cos (+ x eps)) (cos x))
24.0ms	(cos (+ x eps))

simplify2.7s

Counts

30 → 30

Iterations

Useful iterations: 4 (428.0ms)

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: 0.5b

localize38.0ms

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)))
3.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite342.0ms

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:

138.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
35.0ms	(+ (+ x eps) x)
111.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
55.0ms	(sin (/ (+ (+ x eps) x) 2))

series291.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
44.0ms	(+ (+ x eps) x)
82.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
40.0ms	(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

prune313.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite325.0ms

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-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

29.0ms	(* -2 (sin (/ eps 2)))
58.0ms	(+ (+ x eps) x)
150.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
84.0ms	(sin (/ (+ (+ x eps) x) 2))

series200.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* -2 (sin (/ eps 2)))
25.0ms	(+ (+ x eps) x)
100.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
48.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.3s

Counts

70 → 70

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	117	877
1	280	850
2	803	726
3	2345	706
done	5000	700

prune306.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
3.0b	(sin (/ (+ (+ x eps) x) 2))
3.0b	(sin (/ (+ (+ x eps) x) 2))
3.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite234.0ms

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)))
85.0ms	(sin (/ (+ (+ x eps) x) 2))
52.0ms	(sin (/ (+ (+ x eps) x) 2))
61.0ms	(sin (/ (+ (+ x eps) x) 2))

series275.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
35.0ms	(sin (/ (+ (+ x eps) x) 2))
56.0ms	(sin (/ (+ (+ x eps) x) 2))
53.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.9s

Counts

44 → 44

Iterations

Useful iterations: 4 (550.0ms)

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

prune189.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.4b

regimes296.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.4b

bsearch232.0ms

Steps

Iters	Range		Point
9	1.4060273304929084e-10	2.5854593811968635e-05	2.5594022594734032e-05
10	-30636816361710.875	-0.013787396536050121	-0.01398185726995361

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.0s	4485×	body	1280	valid
1.6s	1862×	body	640	valid
906.0ms	603×	body	2560	valid
207.0ms	675×	body	320	valid
104.0ms	289×	body	160	valid
7.0ms	86×	body	80	valid