Details

sample151.0ms

Algorithm

intervals

Results

74.0ms	100×	body	1280	valid
26.0ms	62×	body	640	valid
20.0ms	14×	body	2560	valid
8.0ms	22×	body	320	valid
4.0ms	42×	body	80	valid
3.0ms	16×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize412.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.0b	(sin (+ x eps))

rewrite99.0ms

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:

82.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series109.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(- (sin (+ x eps)) (sin x))
35.0ms	(sin (+ x eps))

simplify5.3s

Counts

46 → 46

Iterations

Useful iterations: 4 (3.1s)

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

prune158.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

46.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
24.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series206.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
83.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
46.0ms	(cos (/ (fma 2 x eps) 2))

simplify6.3s

Counts

60 → 60

Iterations

Useful iterations: done (6.3s)

Iter	Nodes	Cost
0	97	961
1	226	945
2	641	803
3	1880	800
4	4374	784
done	5000	783

prune275.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (fma 2 x eps) 2)))
2.9b	(cos (/ (fma 2 x eps) 2))
2.9b	(cos (/ (fma 2 x eps) 2))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite18.0ms

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:

1.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))
4.0ms	(cos (/ (fma 2 x eps) 2))
8.0ms	(cos (/ (fma 2 x eps) 2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
43.0ms	(cos (/ (fma 2 x eps) 2))
45.0ms	(cos (/ (fma 2 x eps) 2))
34.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.9s

Counts

52 → 52

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	43	563
1	82	552
2	163	486
3	328	479
4	695	463
5	1133	463
6	2174	463
done	5000	435

prune249.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
0.4b	(* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
0.5b	(* (sqrt 2) (* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

14.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
27.0ms	(* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
99.0ms	(* (sqrt 2) (* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))))
9.0ms	(cos (/ (fma 2 x eps) 2))

series361.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
118.0ms	(* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
154.0ms	(* (sqrt 2) (* (sqrt 2) (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))))
32.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.6s

Counts

93 → 93

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	138	1773
1	346	1613
2	1080	1345
3	3714	1336
done	5000	1315

prune239.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.3b

regimes104.0ms

Accuracy

96.1% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.4b

bsearch144.0ms

Steps

Iters	Range		Point
9	2.4768782891511668e-36	5.237808144920513e-30	5.173054498508759e-30
10	-30636816361710.875	-0.013787396536050121	-0.01398185726995361

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3314×	body	1280	valid
1.1s	603×	body	2560	valid
663.0ms	1844×	body	640	valid
165.0ms	802×	body	320	valid
80.0ms	350×	body	160	valid
78.0ms	1087×	body	80	valid