Details

sample224.0ms

Algorithm

intervals

Results

97.0ms	102×	body	1280	valid
61.0ms	19×	body	2560	valid
32.0ms	51×	body	640	valid
11.0ms	26×	body	320	valid
7.0ms	48×	body	80	valid
3.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize12.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
2.8b	(sin (+ x eps))

rewrite66.0ms

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:

58.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series101.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (sin (+ x eps)) (sin x))
28.0ms	(sin (+ x eps))

simplify1.2s

Counts

48 → 48

Iterations

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

prune177.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0b	(cos (/ (fma 2 x eps) 2))

rewrite16.0ms

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:

11.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
5.0ms	(cos (/ (fma 2 x eps) 2))

series113.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.3s

Counts

38 → 38

Iterations

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

prune243.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (/ (fma 2 x eps) 2)) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
3.0b	(cos (/ (fma 2 x eps) 2))
3.0b	(cos (/ (fma 2 x eps) 2))
3.0b	(cos (/ (fma 2 x eps) 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 44

Calls

4 calls:

18.0ms	(cbrt (* (* (cos (/ (fma 2 x eps) 2)) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
5.0ms	(cos (/ (fma 2 x eps) 2))
5.0ms	(cos (/ (fma 2 x eps) 2))
5.0ms	(cos (/ (fma 2 x eps) 2))

series129.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (* (* (cos (/ (fma 2 x eps) 2)) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
26.0ms	(cos (/ (fma 2 x eps) 2))
41.0ms	(cos (/ (fma 2 x eps) 2))
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	2005
5	2005
4	988
3	367
2	137
1	75
0	46

prune452.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (fma 2 x eps) 2)))
3.0b	(cos (/ (fma 2 x eps) 2))
3.0b	(cos (/ (fma 2 x eps) 2))
3.0b	(cos (/ (fma 2 x eps) 2))

rewrite21.0ms

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))

series229.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
33.0ms	(cos (/ (fma 2 x eps) 2))
39.0ms	(cos (/ (fma 2 x eps) 2))
37.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.5s

Counts

56 → 56

Iterations

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

prune351.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes634.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 14.7b

bsearch241.0ms

Steps

Iters	Range		Point
10	1.2035886760163307e-31	1.514112904485791e-15	1.4909178493851906e-15
10	-0.005838610583870787	-4.910260011938944e-13	-7.672969354734922e-09

simplify10.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.7s	3290×	body	1280	valid
1.8s	1869×	body	640	valid
1.1s	641×	body	2560	valid
428.0ms	747×	body	320	valid
134.0ms	1112×	body	80	valid
83.0ms	341×	body	160	valid