Details

sample172.0ms

Algorithm

intervals

Results

97.0ms	149×	body	1280	valid
32.0ms	23×	body	2560	valid
18.0ms	51×	body	640	valid
7.0ms	22×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	2×	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: 39.8b

localize19.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ eps x)) (cos x))
3.4b	(cos (+ eps x))

rewrite37.0ms

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 (+ eps x)) (cos x))
8.0ms	(cos (+ eps x))

series138.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(- (cos (+ eps x)) (cos x))
27.0ms	(cos (+ eps x))

simplify687.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1148
2	352
1	131
0	65

prune189.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2))))
0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
3.5b	(sin (/ (+ (+ x eps) x) 2))

rewrite323.0ms

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-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

96.0ms	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2))))
22.0ms	(+ (+ x eps) x)
134.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
69.0ms	(sin (/ (+ (+ x eps) x) 2))

series326.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2))))
39.0ms	(+ (+ x eps) x)
117.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
37.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify598.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1165
1	286
0	118

prune420.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize50.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (+ (+ x eps) x) 2)) (* (sin (/ eps 2)) -2))
3.5b	(sin (/ (+ (+ x eps) x) 2))

rewrite195.0ms

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-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-r` `*-commutative` `flip-+`

Counts

3 → 40

Calls

3 calls:

29.0ms	(+ (+ x eps) x)
128.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (* (sin (/ eps 2)) -2))
36.0ms	(sin (/ (+ (+ x eps) x) 2))

series205.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (+ x eps) x)
132.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (* (sin (/ eps 2)) -2))
45.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	5004
3	4658
2	768
1	220
0	89

prune334.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
3.5b	(sin (/ (+ (+ x eps) x) 2))
3.5b	(sin (/ (+ (+ x eps) x) 2))
3.5b	(sin (/ (+ x (+ x eps)) 2))

rewrite135.0ms

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:

14.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
43.0ms	(sin (/ (+ (+ x eps) x) 2))
38.0ms	(sin (/ (+ (+ x eps) x) 2))
39.0ms	(sin (/ (+ x (+ x eps)) 2))

series241.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
37.0ms	(sin (/ (+ (+ x eps) x) 2))
37.0ms	(sin (/ (+ (+ x eps) x) 2))
33.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify580.0ms

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
3	1091
2	328
1	136
0	67

prune360.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes301.0ms

Accuracy

96.6% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.2b

bsearch260.0ms

Steps

Iters	Range		Point
10	257785.57693934403	2.1403836343929554e+18	260530.5202352258
11	-496427297.3881253	-4.632829109756021e-12	-8.608808965388138e-05

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.6s	4372×	body	1280	valid
1.4s	1910×	body	640	valid
1.1s	622×	body	2560	valid
199.0ms	733×	body	320	valid
102.0ms	290×	body	160	valid
7.0ms	73×	body	80	valid