Details

sample187.0ms

Algorithm

intervals

Results

98.0ms	106×	body	1280	valid
31.0ms	19×	body	2560	valid
30.0ms	57×	body	640	valid
9.0ms	30×	body	320	valid
4.0ms	36×	body	80	valid
1.0ms	8×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize26.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (sin (+ x eps)) (sin x))
2.8b	(sin (+ x eps))

rewrite71.0ms

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` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

62.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series103.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(- (sin (+ x eps)) (sin x))
27.0ms	(sin (+ x eps))

simplify2.8s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	4407
4	1723
3	751
2	308
1	137
0	65

prune185.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize50.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
2.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

30.0ms	(+ x (+ x eps))
46.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
63.0ms	(cos (/ (+ x (+ x eps)) 2))

series145.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ x (+ x eps))
62.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.1s

Counts

53 → 53

Iterations

Iter	Nodes
done	5004
3	2890
2	654
1	221
0	92

prune343.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.3b	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.4b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
2.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 65

Calls

4 calls:

48.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
78.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
108.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
59.0ms	(cos (/ (+ x (+ x eps)) 2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
60.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
32.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5006
4	3634
3	1389
2	517
1	231
0	109

prune487.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
0.7b	(log (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
2.9b	(cos (/ (+ x (+ x eps)) 2))
2.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod` `log-pow`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `sqrt-pow1`
6×	`exp-prod` `add-exp-log` `sqrt-prod`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow1/2` `rem-log-exp`

Counts

4 → 58

Calls

4 calls:

58.0ms	(log (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
84.0ms	(log (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
56.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))

series280.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(log (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
114.0ms	(log (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
25.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify3.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
5	3552
4	1117
3	461
2	197
1	120
0	70

prune494.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

regimes230.0ms

Accuracy

96.8% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 14.5b

bsearch195.0ms

Steps

Iters	Range		Point
7	8.635844677648429e-30	2.196855215494652e-27	2.1464224965526296e-27
10	-1.4244285555183042e-05	-9.550132857780223e-23	-7.141151458641036e-09

simplify13.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.6s	3276×	body	1280	valid
1.1s	658×	body	2560	valid
1.1s	1801×	body	640	valid
248.0ms	769×	body	320	valid
158.0ms	1144×	body	80	valid
73.0ms	352×	body	160	valid