Details

sample261.0ms

Algorithm

intervals

Results

124.0ms	94×	body	1280	valid
57.0ms	29×	body	2560	valid
42.0ms	56×	body	640	valid
13.0ms	26×	body	320	valid
8.0ms	44×	body	80	valid
3.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite113.0ms

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:

97.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series92.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify1.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	2012
4	2012
3	1269
2	446
1	203
0	92

prune539.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

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))

rewrite17.0ms

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:

13.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series117.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
done	2036
4	2036
3	983
2	353
1	150
0	70

prune394.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize37.0ms

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))

rewrite14.0ms

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)))
5.0ms	(cos (/ (fma 2 x eps) 2))
3.0ms	(cos (/ (fma 2 x eps) 2))
3.0ms	(cos (/ (fma 2 x eps) 2))

series263.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
31.0ms	(cos (/ (fma 2 x eps) 2))
44.0ms	(cos (/ (fma 2 x eps) 2))
42.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.6s

Counts

56 → 56

Iterations

Iter	Nodes
done	2010
5	2010
4	1809
3	590
2	192
1	84
0	45

prune894.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize78.0ms

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))

rewrite11.0ms

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))
4.0ms	(cos (/ (fma 2 x eps) 2))

series191.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))
27.0ms	(cos (/ (fma 2 x eps) 2))
32.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	2001
5	2001
4	1796
3	606
2	203
1	98
0	47

prune761.0ms

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

bsearch277.0ms

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
done	32
1	32
0	24

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.7s	3237×	body	1280	valid
1.9s	1892×	body	640	valid
1.1s	640×	body	2560	valid
456.0ms	759×	body	320	valid
168.0ms	1099×	body	80	valid
95.0ms	373×	body	160	valid