Details

sample196.0ms

Algorithm

intervals

Results

93.0ms	140×	body	1280	valid
50.0ms	60×	body	640	valid
26.0ms	17×	body	2560	valid
7.0ms	25×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	5×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize24.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

12.0ms	(- (cos (+ x eps)) (cos x))
13.0ms	(cos (+ x eps))

series111.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(- (cos (+ x eps)) (cos x))
48.0ms	(cos (+ x eps))

simplify980.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1232
2	337
1	135
0	65

prune211.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
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-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

84.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
13.0ms	(+ x (+ x eps))
101.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
48.0ms	(sin (/ (+ x (+ x eps)) 2))

series323.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
36.0ms	(+ x (+ x eps))
119.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
39.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify972.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1135
1	288
0	118

prune430.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (* -2 (sin (/ (+ x (+ x eps)) 2))) (sin (/ eps 2)))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

19.0ms	(+ x (+ x eps))
73.0ms	(* (* -2 (sin (/ (+ x (+ x eps)) 2))) (sin (/ eps 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))

series192.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ x (+ x eps))
115.0ms	(* (* -2 (sin (/ (+ x (+ x eps)) 2))) (sin (/ eps 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.0s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
2	1155
1	240
0	94

prune314.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.1b	(sin (/ (+ x (+ x eps)) 2))
3.1b	(sin (/ (+ x (+ x eps)) 2))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

15.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
31.0ms	(sin (/ (+ x (+ x eps)) 2))
44.0ms	(sin (/ (+ x (+ x eps)) 2))
29.0ms	(sin (/ (+ x (+ x eps)) 2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
54.0ms	(sin (/ (+ x (+ x eps)) 2))
42.0ms	(sin (/ (+ x (+ x eps)) 2))
52.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify3.2s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
4	4851
3	1071
2	308
1	121
0	57

prune291.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes252.0ms

Accuracy

94.6% (0.8b remaining)

Error of 1.2b against oracle of 0.4b and baseline of 15.8b

bsearch229.0ms

Steps

Iters	Range		Point
11	2.0892179653459966e-19	4.9803363081918155	2.5060963494502007e-05
7	-84463.33967257517	-1026.6337297585196	-1051.778674885963

simplify35.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.3s	4431×	body	1280	valid
1.3s	650×	body	2560	valid
1.2s	1841×	body	640	valid
191.0ms	743×	body	320	valid
44.0ms	255×	body	160	valid
7.0ms	80×	body	80	valid