Details

sample131.0ms

Algorithm

intervals

Results

69.0ms	115×	body	1280	valid
19.0ms	50×	body	640	valid
17.0ms	14×	body	2560	valid
7.0ms	28×	body	320	valid
3.0ms	15×	body	160	valid
3.0ms	34×	body	80	valid

simplify8.0ms

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: 36.5b

localize25.0ms

Local error

Found 2 expressions with local error:

1.8b	(sin (+ x eps))
2.0b	(- (sin (+ x eps)) (sin x))

rewrite128.0ms

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:

15.0ms	(sin (+ x eps))
112.0ms	(- (sin (+ x eps)) (sin x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(sin (+ x eps))
58.0ms	(- (sin (+ x eps)) (sin x))

simplify2.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3921
3	1287
2	461
1	204
0	92

prune179.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
2.1b	(cos (/ (fma 2 x eps) 2))

rewrite19.0ms

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` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

11.0ms	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
7.0ms	(cos (/ (fma 2 x eps) 2))

series113.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2)))
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.0s

Counts

37 → 37

Iterations

Iter	Nodes
done	5004
4	2998
3	971
2	328
1	138
0	64

prune228.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
2.1b	(cos (/ (fma 2 x eps) 2))
2.1b	(cos (/ (fma 2 x eps) 2))
2.1b	(cos (/ (fma 2 x eps) 2))

rewrite30.0ms

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` `pow1/3`

Counts

4 → 42

Calls

4 calls:

9.0ms	(cbrt (* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
7.0ms	(cos (/ (fma 2 x eps) 2))
6.0ms	(cos (/ (fma 2 x eps) 2))
7.0ms	(cos (/ (fma 2 x eps) 2))

series319.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
43.0ms	(cos (/ (fma 2 x eps) 2))
44.0ms	(cos (/ (fma 2 x eps) 2))
51.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.0s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
4	2715
3	806
2	257
1	130
0	65

prune320.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
2.1b	(cos (/ (fma 2 x eps) 2))
2.1b	(cos (/ (fma 2 x eps) 2))
2.1b	(cos (/ (fma 2 x eps) 2))

rewrite13.0ms

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` `pow1/3`

Counts

4 → 42

Calls

4 calls:

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

series211.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (* (cos (/ (fma 2 x eps) 2)) (sin (/ eps 2))))
36.0ms	(cos (/ (fma 2 x eps) 2))
30.0ms	(cos (/ (fma 2 x eps) 2))
25.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.1s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
4	2715
3	806
2	257
1	130
0	65

prune302.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.6b

regimes126.0ms

Accuracy

98.3% (0.3b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.3b

bsearch142.0ms

Steps

Iters	Range		Point
8	6.0329627772416755e-24	1.9249297628844816e-20	1.8942327691411048e-20
9	-5.984165099293203e-09	-2.0017119239229129e-16	-5.893930927518443e-09

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.4s	3310×	body	1280	valid
1.0s	618×	body	2560	valid
857.0ms	1858×	body	640	valid
164.0ms	764×	body	320	valid
78.0ms	1111×	body	80	valid
49.0ms	339×	body	160	valid