Details

sample154.0ms

Algorithm

intervals

Results

74.0ms	100×	body	1280	valid
29.0ms	62×	body	640	valid
19.0ms	14×	body	2560	valid
7.0ms	22×	body	320	valid
5.0ms	42×	body	80	valid
3.0ms	16×	body	160	valid

simplify8.0ms

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: 33.8b

localize18.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.0b	(sin (+ x eps))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

53.0ms	(- (sin (+ x eps)) (sin x))
38.0ms	(sin (+ x eps))

series81.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify3.1s

Counts

30 → 30

Iterations

Useful iterations: 4 (528.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	284	281
3	572	275
4	1162	271
5	2763	271
done	5000	271

prune98.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
2.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite160.0ms

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-cos-mult`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

42.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
30.0ms	(+ (+ x eps) x)
26.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
58.0ms	(cos (/ (+ (+ x eps) x) 2))

series207.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
24.0ms	(+ (+ x eps) x)
61.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
40.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	118	1100
1	292	1077
2	819	917
3	2476	893
done	5000	885

prune275.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
2.9b	(cos (/ (+ (+ x eps) x) 2))
2.9b	(cos (/ (+ (+ x eps) x) 2))
2.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite189.0ms

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:

2.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
77.0ms	(cos (/ (+ (+ x eps) x) 2))
52.0ms	(cos (/ (+ (+ x eps) x) 2))
58.0ms	(cos (/ (+ (+ x eps) x) 2))

series252.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
42.0ms	(cos (/ (+ (+ x eps) x) 2))
45.0ms	(cos (/ (+ (+ x eps) x) 2))
48.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.5s

Counts

44 → 44

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	42	551
1	88	540
2	162	466
3	289	447
4	509	447
5	831	447
6	1833	447
done	5000	415

prune283.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
0.4b	(* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
0.5b	(* (sqrt 2) (* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))))
2.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`associate-l`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`sqrt-prod`
5×	`associate-r`
4×	`add-log-exp`
3×	`associate-r/` `-commutative` `sin-cos-mult`
1×	`unswap-sqr`

Counts

4 → 73

Calls

4 calls:

24.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
35.0ms	(* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
115.0ms	(* (sqrt 2) (* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))))
62.0ms	(cos (/ (+ (+ x eps) x) 2))

series430.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
161.0ms	(* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
170.0ms	(* (sqrt 2) (* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))))
32.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.7s

Counts

85 → 85

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	133	1765
1	341	1616
2	1038	1328
3	3659	1301
done	5001	1292

prune207.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.3b

regimes116.0ms

Accuracy

96.1% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.4b

bsearch188.0ms

Steps

Iters	Range		Point
9	2.4768782891511668e-36	5.237808144920513e-30	5.173054498508759e-30
10	-30636816361710.875	-0.013787396536050121	-0.01398185726995361

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	25	51
1	35	38
done	35	38

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.6s	3314×	body	1280	valid
1.3s	603×	body	2560	valid
887.0ms	1844×	body	640	valid
311.0ms	802×	body	320	valid
79.0ms	1087×	body	80	valid
55.0ms	350×	body	160	valid