Details

sample147.0ms

Algorithm

intervals

Results

72.0ms	143×	body	1280	valid
33.0ms	25×	body	2560	valid
17.0ms	50×	body	640	valid
7.0ms	29×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	1×	body	80	valid

simplify7.0ms

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: 42.2b

localize72.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite38.0ms

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))
15.0ms	(cos (+ x eps))

series110.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (cos (+ x eps)) (cos x))
30.0ms	(cos (+ x eps))

simplify2.6s

Counts

30 → 30

Iterations

Iter	Nodes
done	5015
5	4022
4	1465
3	652
2	280
1	135
0	65

prune148.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

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)))
3.7b	(sin (/ (+ x (+ x eps)) 2))

rewrite211.0ms

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:

99.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
21.0ms	(+ x (+ x eps))
56.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
32.0ms	(sin (/ (+ x (+ x eps)) 2))

series362.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
42.0ms	(+ x (+ x eps))
103.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
53.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3797
2	858
1	287
0	118

prune470.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

localize81.0ms

Local error

Found 4 expressions with local error:

3.7b	(sin (/ (+ x (+ x eps)) 2))
6.2b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
6.2b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
6.2b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

rewrite83.0ms

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:

29.0ms	(sin (/ (+ x (+ x eps)) 2))
21.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
17.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
15.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sin (/ (+ x (+ x eps)) 2))
195.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
181.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
194.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

simplify2.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	5002
4	2806
3	772
2	284
1	138
0	68

prune418.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.4b

localize100.0ms

Local error

Found 4 expressions with local error:

3.7b	(sin (/ (+ x (+ x eps)) 2))
6.2b	(cbrt (* (* (* (cbrt (sin (/ (+ x (+ x eps)) 2))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2))))
6.2b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
6.2b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

rewrite661.0ms

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` `pow1/3`
2×	`cbrt-div` `sin-mult`

Counts

4 → 36

Calls

4 calls:

24.0ms	(sin (/ (+ x (+ x eps)) 2))
582.0ms	(cbrt (* (* (* (cbrt (sin (/ (+ x (+ x eps)) 2))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2))))
29.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
24.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sin (/ (+ x (+ x eps)) 2))
172.0ms	(cbrt (* (* (* (cbrt (sin (/ (+ x (+ x eps)) 2))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2))))
167.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
143.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

simplify2.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5002
4	3018
3	821
2	310
1	154
0	79

prune456.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.4b

regimes299.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch219.0ms

Steps

Iters	Range		Point
8	9.663324920224664e-10	1.054768169099283e-06	1.0360142885107461e-06
10	-2.725519985046895e-08	-4.357977289634356e-25	-2.6849380613362534e-08

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	4429×	body	1280	valid
1.0s	671×	body	2560	valid
924.0ms	1838×	body	640	valid
294.0ms	710×	body	320	valid
50.0ms	284×	body	160	valid
6.0ms	68×	body	80	valid