Details

sample279.0ms

Algorithm

intervals

Results

117.0ms	106×	body	1280	valid
80.0ms	55×	body	640	valid
44.0ms	24×	body	2560	valid
15.0ms	30×	body	320	valid
5.0ms	31×	body	80	valid
4.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize19.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (sin (+ x eps)) (sin x))
5.0b	(sin (+ x eps))

rewrite64.0ms

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:

56.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series68.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify1.2s

Counts

32 → 32

Iterations

Iter	Nodes
5	3343
4	1447
3	634
2	296
1	137
0	65

prune253.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
5.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite54.0ms

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:

11.0ms	(+ x (+ x eps))
24.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
19.0ms	(cos (/ (+ x (+ x eps)) 2))

series146.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ x (+ x eps))
65.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
38.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify4.1s

Counts

53 → 53

Iterations

Iter	Nodes
4	6965
3	1694
2	567
1	224
0	94

prune573.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (cos (+ (* eps 1/2) x)) (sin (* eps 1/2)))
5.1b	(cos (+ (* eps 1/2) x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`insert-posit16` `add-log-exp`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

23.0ms	(* (cos (+ (* eps 1/2) x)) (sin (* eps 1/2)))
24.0ms	(cos (+ (* eps 1/2) x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(* (cos (+ (* eps 1/2) x)) (sin (* eps 1/2)))
28.0ms	(cos (+ (* eps 1/2) x))

simplify1.5s

Counts

34 → 34

Iterations

Iter	Nodes
5	2943
4	1412
3	741
2	313
1	133
0	66

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* eps 1/2)) (cos x))
0.1b	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
0.2b	(* (sin (* eps 1/2)) (sin x))
0.3b	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* eps 1/2)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`associate-*l/` `insert-posit16`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log`

Counts

4 → 78

Calls

4 calls:

16.0ms	(* (cos (* eps 1/2)) (cos x))
34.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
22.0ms	(* (sin (* eps 1/2)) (sin x))
130.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* eps 1/2)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos (* eps 1/2)) (cos x))
101.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
59.0ms	(* (sin (* eps 1/2)) (sin x))
167.0ms	(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* eps 1/2)))

simplify999.0ms

Counts

90 → 90

Iterations

Iter	Nodes
3	3365
2	1015
1	337
0	145

prune773.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	23
1	23
0	17

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.4s	3278×	body	1280	valid
1.2s	617×	body	2560	valid
978.0ms	1828×	body	640	valid
359.0ms	795×	body	320	valid
178.0ms	1120×	body	80	valid
99.0ms	362×	body	160	valid