Details

sample135.0ms

Algorithm

intervals

Results

64.0ms	113×	body	1280	valid
22.0ms	18×	body	2560	valid
20.0ms	60×	body	640	valid
6.0ms	10×	body	160	valid
6.0ms	23×	body	320	valid
2.0ms	32×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize15.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite88.0ms

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

Counts

2 → 40

Calls

2 calls:

66.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

series85.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (sin (+ x eps)) (sin x))
30.0ms	(sin (+ x eps))

simplify4.8s

Counts

46 → 46

Iterations

Useful iterations: 4 (2.9s)

Iter	Nodes	Cost
0	91	662
1	194	539
2	450	452
3	1388	388
4	4919	374
done	5000	374

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.4b	(cos (/ (fma 2 x eps) 2))

rewrite31.0ms

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` `sin-cos-mult` `cbrt-unprod` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

25.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
5.0ms	(cos (/ (fma 2 x eps) 2))

series116.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
47.0ms	(cos (/ (fma 2 x eps) 2))

simplify4.2s

Counts

36 → 36

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	68	514
1	144	508
2	341	444
3	687	442
4	1340	431
5	2510	431
done	5001	430

prune133.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
0.4b	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
3.4b	(cos (/ (fma 2 x eps) 2))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

33.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
3.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
3.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
4.0ms	(cos (/ (fma 2 x eps) 2))

series158.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
25.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
57.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.0s

Counts

105 → 105

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	122	1694
1	250	1400
2	721	1252
3	3866	1232
done	5000	1231

prune259.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(log1p (pow (cos (/ (fma 2 x eps) 2)) 3))
0.4b	(cbrt (expm1 (log1p (pow (cos (/ (fma 2 x eps) 2)) 3))))
0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
3.4b	(cos (/ (fma 2 x eps) 2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube`
4×	`log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `log1p-udef` `pow-pow` `pow1/3` `unpow3` `log1p-expm1` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 58

Calls

4 calls:

1.0ms	(log1p (pow (cos (/ (fma 2 x eps) 2)) 3))
1.0ms	(cbrt (expm1 (log1p (pow (cos (/ (fma 2 x eps) 2)) 3))))
4.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
4.0ms	(cos (/ (fma 2 x eps) 2))

series320.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(log1p (pow (cos (/ (fma 2 x eps) 2)) 3))
151.0ms	(cbrt (expm1 (log1p (pow (cos (/ (fma 2 x eps) 2)) 3))))
54.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.9s

Counts

70 → 70

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	90	954
1	187	784
2	469	688
3	2404	680
done	5001	664

prune203.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.5b

regimes134.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.0b

bsearch100.0ms

Steps

Iters	Range		Point
11	3.560853546224578e-32	4.11075536510938e-11	4.0610401173791624e-11
6	-1.6640733670284383e-05	-3.4900073017642136e-06	-3.523695819775611e-06

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	50
1	32	37
done	32	37

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	3326×	body	1280	valid
610.0ms	673×	body	2560	valid
486.0ms	1887×	body	640	valid
114.0ms	706×	body	320	valid
63.0ms	1078×	body	80	valid
36.0ms	330×	body	160	valid