Details

sample186.0ms

Algorithm

intervals

Results

97.0ms	145×	body	1280	valid
28.0ms	65×	body	640	valid
24.0ms	14×	body	2560	valid
18.0ms	22×	body	320	valid
2.0ms	7×	body	160	valid
0.0ms	3×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite76.0ms

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:

54.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

series121.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(- (cos (+ x eps)) (cos x))
42.0ms	(cos (+ x eps))

simplify638.0ms

Counts

30 → 30

Iterations

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

prune204.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

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)))
2.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite241.0ms

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:

78.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
14.0ms	(+ x (+ x eps))
101.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
45.0ms	(sin (/ (+ x (+ x eps)) 2))

series362.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
41.0ms	(+ x (+ x eps))
107.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
47.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify627.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1135
1	288
0	118

prune496.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ eps (* 2 x)) 2)))
2.9b	(sin (/ (+ eps (* 2 x)) 2))

rewrite79.0ms

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:

63.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ eps (* 2 x)) 2)))
15.0ms	(sin (/ (+ eps (* 2 x)) 2))

series129.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ eps (* 2 x)) 2)))
31.0ms	(sin (/ (+ eps (* 2 x)) 2))

simplify846.0ms

Counts

31 → 31

Iterations

Iter	Nodes
done	5001
2	826
1	169
0	69

prune205.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

2.9b	(sin (/ (+ eps (* 2 x)) 2))
6.8b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))
6.8b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))
6.8b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))

rewrite37.0ms

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`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`

Counts

4 → 37

Calls

4 calls:

8.0ms	(sin (/ (+ eps (* 2 x)) 2))
7.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))
9.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))
12.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sin (/ (+ eps (* 2 x)) 2))
198.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))
235.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))
206.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ eps (* 2 x)) 2))))

simplify766.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
3	1196
2	323
1	132
0	65

prune446.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.3b

regimes502.0ms

Accuracy

96.2% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.0b

bsearch172.0ms

Steps

Iters	Range		Point
9	6968.3439428623215	12923530959.442633	7051.556907543755
8	-72632609.50044116	-1138.2876542095912	-1170.229056579155

simplify5.0ms

Iterations

Iter	Nodes
done	41
2	41
1	40
0	28

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.2s	4460×	body	1280	valid
1.1s	652×	body	2560	valid
831.0ms	1851×	body	640	valid
258.0ms	693×	body	320	valid
54.0ms	291×	body	160	valid
5.0ms	53×	body	80	valid