Details

sample241.0ms

Algorithm

intervals

Results

144.0ms	112×	body	1280	valid
35.0ms	20×	body	2560	valid
30.0ms	52×	body	640	valid
11.0ms	25×	body	320	valid
4.0ms	15×	body	160	valid
4.0ms	32×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite73.0ms

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` `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))
6.0ms	(sin (+ x eps))

series76.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(sin (+ x eps))

simplify2.1s

Counts

46 → 46

Iterations

Iter	Nodes
4	3327
3	1146
2	429
1	199
0	90

prune446.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.2b	(cos (/ (fma 2 x eps) 2))

rewrite14.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

10.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series105.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
43.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.6s

Counts

36 → 36

Iterations

Iter	Nodes
5	3146
4	1789
3	797
2	336
1	146
0	68

prune412.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.2b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.4b	(expm1 (cos (/ (fma 2 x eps) 2)))
3.2b	(cos (/ (fma 2 x eps) 2))

rewrite13.0ms

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` `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 → 51

Calls

4 calls:

9.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
84.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
59.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
30.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.4s

Counts

63 → 63

Iterations

Iter	Nodes
4	2293
3	1029
2	455
1	199
0	93

prune742.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (cos (/ (fma x 2 eps) 2)) (* (cos (/ (fma x 2 eps) 2)) (cos (/ (fma x 2 eps) 2)))))
3.2b	(cos (/ (fma x 2 eps) 2))
3.2b	(cos (/ (fma x 2 eps) 2))
3.2b	(cos (/ (fma x 2 eps) 2))

rewrite33.0ms

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` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `cube-unmult` `associate-*r/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 40

Calls

4 calls:

19.0ms	(cbrt (* (cos (/ (fma x 2 eps) 2)) (* (cos (/ (fma x 2 eps) 2)) (cos (/ (fma x 2 eps) 2)))))
8.0ms	(cos (/ (fma x 2 eps) 2))
3.0ms	(cos (/ (fma x 2 eps) 2))
3.0ms	(cos (/ (fma x 2 eps) 2))

series167.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt (* (cos (/ (fma x 2 eps) 2)) (* (cos (/ (fma x 2 eps) 2)) (cos (/ (fma x 2 eps) 2)))))
43.0ms	(cos (/ (fma x 2 eps) 2))
43.0ms	(cos (/ (fma x 2 eps) 2))
46.0ms	(cos (/ (fma x 2 eps) 2))

simplify6.1s

Counts

52 → 52

Iterations

Iter	Nodes
8	4022
7	1673
6	1101
5	843
4	590
3	324
2	145
1	78
0	45

prune650.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.5b

regimes275.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.8b

bsearch228.0ms

Steps

Iters	Range		Point
9	2.856347663939308e-08	0.9676876931049737	3.970291838078694e-08
8	-1.3860482868045466e-05	-3.3361098338481354e-09	-2.7134465698925543e-08

simplify10.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.0s	3309×	body	1280	valid
1.8s	1873×	body	640	valid
1.3s	624×	body	2560	valid
459.0ms	765×	body	320	valid
240.0ms	1107×	body	80	valid
119.0ms	322×	body	160	valid