Details

sample145.0ms

Algorithm

intervals

Results

69.0ms	111×	body	1280	valid
26.0ms	20×	body	2560	valid
23.0ms	56×	body	640	valid
6.0ms	23×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	202
1	9	202
2	10	202
done	10	202

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
2.3b	(sin (+ x eps))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

91.0ms	(- (sin (+ x eps)) (sin x))
16.0ms	(sin (+ x eps))

series111.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify1.1s

Counts

30 → 30

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	63	8462
1	135	7579
2	381	7579
3	1449	7539
done	5001	7459

prune189.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(/ (+ (+ x eps) x) 2)
0.3b	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
2.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

37.0ms	(+ (+ x eps) x)
87.0ms	(/ (+ (+ x eps) x) 2)
23.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
73.0ms	(cos (/ (+ (+ x eps) x) 2))

series231.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (+ x eps) x)
50.0ms	(/ (+ (+ x eps) x) 2)
116.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
32.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify920.0ms

Counts

89 → 89

Iterations

Useful iterations: done (911.0ms)

Iter	Nodes	Cost
0	128	23186
1	302	21487
2	1328	21367
done	5000	21043

prune482.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (/ (+ (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2))) (cos (/ (+ (+ x eps) x) 2))))
2.5b	(cos (/ (+ (+ x eps) x) 2))
2.5b	(cos (/ (+ (+ x eps) x) 2))
2.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite137.0ms

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/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 32

Calls

4 calls:

13.0ms	(cbrt (* (* (cos (/ (+ (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2))) (cos (/ (+ (+ x eps) x) 2))))
36.0ms	(cos (/ (+ (+ x eps) x) 2))
47.0ms	(cos (/ (+ (+ x eps) x) 2))
40.0ms	(cos (/ (+ (+ x eps) x) 2))

series121.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (* (* (cos (/ (+ (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2))) (cos (/ (+ (+ x eps) x) 2))))
33.0ms	(cos (/ (+ (+ x eps) x) 2))
25.0ms	(cos (/ (+ (+ x eps) x) 2))
30.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.0s

Counts

44 → 44

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	43	12566
1	79	11623
2	174	11463
3	615	10014
4	2796	10014
done	5002	9974

prune366.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize89.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ (+ x eps) x) 2))
2.5b	(cos (/ (+ (+ x eps) x) 2))
2.5b	(cos (/ (+ (+ x eps) x) 2))
2.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite168.0ms

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`

Counts

4 → 28

Calls

4 calls:

38.0ms	(cos (/ (+ (+ x eps) x) 2))
40.0ms	(cos (/ (+ (+ x eps) x) 2))
46.0ms	(cos (/ (+ (+ x eps) x) 2))
43.0ms	(cos (/ (+ (+ x eps) x) 2))

series134.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ (+ x eps) x) 2))
38.0ms	(cos (/ (+ (+ x eps) x) 2))
29.0ms	(cos (/ (+ (+ x eps) x) 2))
40.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.5s

Counts

40 → 40

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	26	10256
1	56	9412
2	130	9252
3	434	8924
4	1775	8924
done	5001	8924

prune330.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

regimes258.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.1b

bsearch184.0ms

Steps

Iters	Range		Point
8	2.673612976528507e-11	7.42116589675916e-09	5.463141894552383e-09
9	-3322970397.4786234	-6367.3348759504115	-6443.306290177518

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	1025
1	35	1025
done	35	1025

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.2s	3320×	body	1280	valid
1.5s	1868×	body	640	valid
1.0s	637×	body	2560	valid
327.0ms	725×	body	320	valid
186.0ms	1106×	body	80	valid
73.0ms	344×	body	160	valid