Details

sample251.0ms

Algorithm

intervals

Results

88.0ms	85×	body	1280	valid
75.0ms	20×	body	2560	valid
48.0ms	63×	body	640	valid
15.0ms	29×	body	320	valid
7.0ms	47×	body	80	valid
4.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize14.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
4.3b	(sin (+ x eps))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

65.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series84.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify1.2s

Counts

32 → 32

Iterations

Iter	Nodes
done	2009
5	2009
4	1723
3	751
2	308
1	137
0	65

prune286.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
4.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

19.0ms	(+ x (+ x eps))
20.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

series132.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ x (+ x eps))
61.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
37.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify886.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	2005
3	2005
2	654
1	221
0	92

prune583.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.2b	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
4.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 65

Calls

4 calls:

41.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
41.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
44.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
25.0ms	(cos (/ (+ x (+ x eps)) 2))

series215.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
75.0ms	(* (sin (* 1/2 eps)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
34.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.3s

Counts

77 → 77

Iterations

Iter	Nodes
done	2003
4	2003
3	1389
2	517
1	231
0	109

prune958.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
4.1b	(cos (/ (+ x (+ x eps)) 2))
4.1b	(cos (/ (+ x (+ x eps)) 2))
4.1b	(cos (/ (+ x (+ x eps)) 2))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 36

Calls

4 calls:

23.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
23.0ms	(cos (/ (+ x (+ x eps)) 2))
28.0ms	(cos (/ (+ x (+ x eps)) 2))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

series142.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
37.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))
40.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	2019
5	2019
4	1195
3	396
2	139
1	83
0	45

prune512.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.4b

regimes188.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.2b

bsearch220.0ms

Steps

Iters	Range		Point
8	3.9568734232294605e-09	3.8140973376779237e-06	6.77676751873262e-09
7	-0.35383103211093586	-0.008083691246901765	-0.008247894483255535

simplify11.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.0s	3311×	body	1280	valid
945.0ms	633×	body	2560	valid
827.0ms	1788×	body	640	valid
736.0ms	1123×	body	80	valid
273.0ms	822×	body	320	valid
62.0ms	323×	body	160	valid