Details

sample161.0ms

Algorithm

intervals

Results

79.0ms	140×	body	1280	valid
38.0ms	28×	body	2560	valid
22.0ms	61×	body	640	valid
7.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.6b	(cos (+ x eps))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

28.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series133.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (cos (+ x eps)) (cos x))
46.0ms	(cos (+ x eps))

simplify5.1s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.0s)

Iter	Nodes	Cost
0	91	664
1	194	540
2	439	453
3	1358	389
4	4783	375
done	5000	375

prune146.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
4.4b	(sin (/ (fma 2 x eps) 2))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

39.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
9.0ms	(sin (/ (fma 2 x eps) 2))

series128.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
58.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.1s

Counts

36 → 36

Iterations

Useful iterations: 4 (676.0ms)

Iter	Nodes	Cost
0	70	512
1	141	507
2	336	444
3	652	442
4	1161	433
5	2112	433
6	4904	433
done	5000	433

prune165.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

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)))))
4.4b	(sin (/ (fma 2 x eps) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
20.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
9.0ms	(sin (/ (fma 2 x eps) 2))

series397.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
104.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
155.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
45.0ms	(sin (/ (fma 2 x eps) 2))

simplify6.5s

Counts

63 → 63

Iterations

Useful iterations: 4 (777.0ms)

Iter	Nodes	Cost
0	90	841
1	168	753
2	382	660
3	705	657
4	1226	638
5	2185	638
6	4944	638
done	5000	638

prune367.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (fma 2 x eps) 2)))
4.4b	(sin (/ (fma 2 x eps) 2))
4.4b	(sin (/ (fma 2 x eps) 2))
4.4b	(sin (/ (fma 2 x eps) 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

5.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
9.0ms	(sin (/ (fma 2 x eps) 2))
9.0ms	(sin (/ (fma 2 x eps) 2))
5.0ms	(sin (/ (fma 2 x eps) 2))

series336.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
55.0ms	(sin (/ (fma 2 x eps) 2))
57.0ms	(sin (/ (fma 2 x eps) 2))
71.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.4s

Counts

52 → 52

Iterations

Useful iterations: 5 (2.6s)

Iter	Nodes	Cost
0	58	582
1	116	575
2	250	517
3	572	505
4	1546	480
5	4535	479
done	5000	479

prune358.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes188.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 14.9b

bsearch206.0ms

Steps

Iters	Range		Point
10	2.714148548773617e-15	3495.1882749471233	3.028675491606891e-06
10	-7.35943201301068	-4.7981562703001505e-12	-0.00026844987953330624

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	51
1	33	51
done	33	51

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.3s	4478×	body	1280	valid
986.0ms	1802×	body	640	valid
936.0ms	625×	body	2560	valid
200.0ms	732×	body	320	valid
50.0ms	279×	body	160	valid
8.0ms	84×	body	80	valid