Details

sample226.0ms

Algorithm

intervals

Results

88.0ms	94×	body	1280	valid
53.0ms	56×	body	640	valid
52.0ms	29×	body	2560	valid
12.0ms	26×	body	320	valid
6.0ms	44×	body	80	valid
2.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize26.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (sin (+ x eps)) (sin x))
4.1b	(sin (+ x eps))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

48.0ms	(- (sin (+ x eps)) (sin x))
49.0ms	(sin (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify1.6s

Counts

48 → 48

Iterations

Iter	Nodes
4	3108
3	1127
2	429
1	201
0	92

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite29.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

22.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))

series111.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.6s

Counts

38 → 38

Iterations

Iter	Nodes
5	3026
4	1701
3	796
2	336
1	148
0	70

prune207.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (fma 2 x eps) 2)))
4.1b	(cos (/ (fma 2 x eps) 2))
4.1b	(cos (/ (fma 2 x eps) 2))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))
6.0ms	(cos (/ (fma 2 x eps) 2))
6.0ms	(cos (/ (fma 2 x eps) 2))

series250.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
48.0ms	(cos (/ (fma 2 x eps) 2))
46.0ms	(cos (/ (fma 2 x eps) 2))
46.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.8s

Counts

56 → 56

Iterations

Iter	Nodes
6	2433
5	1409
4	827
3	359
2	160
1	82
0	45

prune378.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (cos (/ (fma 2 x eps) 2)))
4.1b	(cos (/ (fma 2 x eps) 2))
4.1b	(cos (/ (fma 2 x eps) 2))
4.1b	(cos (/ (fma 2 x eps) 2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 42

Calls

4 calls:

0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))
3.0ms	(cos (/ (fma 2 x eps) 2))
3.0ms	(cos (/ (fma 2 x eps) 2))

series206.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
48.0ms	(cos (/ (fma 2 x eps) 2))
43.0ms	(cos (/ (fma 2 x eps) 2))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.8s

Counts

54 → 54

Iterations

Iter	Nodes
5	2320
4	1109
3	456
2	195
1	95
0	47

prune491.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

regimes222.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.4b

bsearch298.0ms

Steps

Iters	Range		Point
10	3.395948864018026e-11	318690.85562629136	1.9528216764299977e-08
11	-0.030639508246526274	-2.729201958508851e-30	-8.778095247816633e-09

simplify10.0ms

Iterations

Iter	Nodes
2	32
1	32
0	24

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.1s	3237×	body	1280	valid
2.4s	1892×	body	640	valid
1.2s	640×	body	2560	valid
371.0ms	759×	body	320	valid
190.0ms	1099×	body	80	valid
131.0ms	373×	body	160	valid