Details

sample162.0ms

Algorithm

intervals

Results

100.0ms	153×	body	1280	valid
24.0ms	20×	body	2560	valid
20.0ms	54×	body	640	valid
4.0ms	14×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	5×	body	80	valid

simplify12.0ms

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: 38.3b

localize26.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite52.0ms

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` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

21.0ms	(- (cos (+ x eps)) (cos x))
30.0ms	(cos (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify1.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	2010
4	2010
3	1158
2	424
1	202
0	93

prune250.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
2.9b	(sin (/ (fma 2 x eps) 2))

rewrite34.0ms

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-mult` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

27.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series106.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
37.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.1s

Counts

38 → 38

Iterations

Iter	Nodes
done	2000
4	2000
3	849
2	332
1	146
0	71

prune266.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (fma 2 x eps) 2)))
0.3b	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
2.9b	(sin (/ (fma 2 x eps) 2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

0.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
10.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
3.0ms	(sin (/ (fma 2 x eps) 2))

series312.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
75.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
137.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
36.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.4s

Counts

67 → 67

Iterations

Iter	Nodes
done	2014
5	2014
4	1974
3	911
2	408
1	185
0	93

prune369.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (fma 2 x eps) 2)))
2.9b	(sin (/ (fma 2 x eps) 2))
2.9b	(sin (/ (fma 2 x eps) 2))
2.9b	(sin (/ (fma 2 x eps) 2))

rewrite12.0ms

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 (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))
3.0ms	(sin (/ (fma 2 x eps) 2))
3.0ms	(sin (/ (fma 2 x eps) 2))

series274.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
43.0ms	(sin (/ (fma 2 x eps) 2))
51.0ms	(sin (/ (fma 2 x eps) 2))
43.0ms	(sin (/ (fma 2 x eps) 2))

simplify942.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2014
4	2014
3	800
2	262
1	117
0	60

prune344.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.4b

regimes292.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch263.0ms

Steps

Iters	Range		Point
10	5.037382729650074e-10	232.09055164250086	2.2247927857601395e-06
10	-1.3816842601692823e-07	-2.482857645479789e-25	-1.347365952010613e-07

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample8.6s

Algorithm

intervals

Results

5.5s	4455×	body	1280	valid
1.2s	1802×	body	640	valid
1.2s	656×	body	2560	valid
341.0ms	719×	body	320	valid
81.0ms	287×	body	160	valid
10.0ms	81×	body	80	valid