Details

sample178.0ms

Algorithm

intervals

Results

84.0ms	133×	body	1280	valid
42.0ms	29×	body	2560	valid
24.0ms	63×	body	640	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	3×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize64.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
2.3b	(cos (+ x eps))

rewrite43.0ms

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:

22.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

series102.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify760.0ms

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

localize27.0ms

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)))
2.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite212.0ms

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:

72.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
20.0ms	(+ x (+ x eps))
83.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
36.0ms	(sin (/ (+ x (+ x eps)) 2))

series358.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
44.0ms	(+ x (+ x eps))
121.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
45.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify579.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1135
1	288
0	118

prune542.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ eps (* 2 x)) 2)))
2.1b	(sin (/ (+ eps (* 2 x)) 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`add-log-exp`
1×	`associate-l` `*-commutative`

Counts

2 → 25

Calls

2 calls:

39.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ eps (* 2 x)) 2)))
8.0ms	(sin (/ (+ eps (* 2 x)) 2))

series133.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ eps (* 2 x)) 2)))
34.0ms	(sin (/ (+ eps (* 2 x)) 2))

simplify765.0ms

Counts

31 → 31

Iterations

Iter	Nodes
done	5001
2	826
1	169
0	69

prune215.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (* x 2) eps) 2)))
2.1b	(sin (/ (+ (* x 2) eps) 2))
2.1b	(sin (/ (+ (* x 2) eps) 2))
2.1b	(sin (/ (+ (* x 2) eps) 2))

rewrite72.0ms

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:

8.0ms	(cbrt (sin (/ (+ (* x 2) eps) 2)))
19.0ms	(sin (/ (+ (* x 2) eps) 2))
25.0ms	(sin (/ (+ (* x 2) eps) 2))
18.0ms	(sin (/ (+ (* x 2) eps) 2))

series301.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (sin (/ (+ (* x 2) eps) 2)))
59.0ms	(sin (/ (+ (* x 2) eps) 2))
56.0ms	(sin (/ (+ (* x 2) eps) 2))
37.0ms	(sin (/ (+ (* x 2) eps) 2))

simplify2.8s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
4	4585
3	1007
2	293
1	117
0	57

prune336.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

regimes447.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.9b

bsearch205.0ms

Steps

Iters	Range		Point
10	6.967356414530657e-12	13.800596953327334	8.703484289726959e-06
7	-22.8286883066892	-0.10952899301968014	-0.11140260853014235

simplify15.0ms

Iterations

Iter	Nodes
done	41
2	41
1	40
0	28

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.4s	4407×	body	1280	valid
2.2s	1935×	body	640	valid
963.0ms	633×	body	2560	valid
183.0ms	655×	body	320	valid
56.0ms	299×	body	160	valid
6.0ms	71×	body	80	valid