Details

sample295.0ms

Algorithm

intervals

Results

120.0ms	106×	body	1280	valid
102.0ms	34×	body	2560	valid
34.0ms	47×	body	640	valid
16.0ms	32×	body	320	valid
5.0ms	12×	body	160	valid
4.0ms	25×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize27.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite86.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

71.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify1.7s

Counts

48 → 48

Iterations

Iter	Nodes
4	3108
3	1127
2	429
1	201
0	92

prune352.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.5b	(cos (/ (fma 2 x eps) 2))

rewrite15.0ms

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-cos-mult` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

12.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series108.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
30.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.5s

Counts

38 → 38

Iterations

Iter	Nodes
5	3026
4	1701
3	796
2	336
1	148
0	70

prune393.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (fma 2 x eps) 2)) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
3.5b	(cos (/ (fma 2 x eps) 2))
3.5b	(cos (/ (fma 2 x eps) 2))
3.5b	(cos (/ (fma 2 x eps) 2))

rewrite46.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 44

Calls

4 calls:

28.0ms	(cbrt (* (* (cos (/ (fma 2 x eps) 2)) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
6.0ms	(cos (/ (fma 2 x eps) 2))
6.0ms	(cos (/ (fma 2 x eps) 2))
6.0ms	(cos (/ (fma 2 x eps) 2))

series137.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt (* (* (cos (/ (fma 2 x eps) 2)) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
32.0ms	(cos (/ (fma 2 x eps) 2))
32.0ms	(cos (/ (fma 2 x eps) 2))
26.0ms	(cos (/ (fma 2 x eps) 2))

simplify6.8s

Counts

56 → 56

Iterations

Iter	Nodes
8	3896
7	1644
6	1104
5	848
4	543
3	265
2	127
1	72
0	46

prune580.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (expm1 (log1p (cos (/ (fma 2 x eps) 2)))) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
3.5b	(cos (/ (fma 2 x eps) 2))
3.5b	(cos (/ (fma 2 x eps) 2))
3.5b	(cos (/ (fma 2 x eps) 2))

rewrite28.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 42

Calls

4 calls:

17.0ms	(cbrt (* (* (expm1 (log1p (cos (/ (fma 2 x eps) 2)))) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
3.0ms	(cos (/ (fma 2 x eps) 2))
3.0ms	(cos (/ (fma 2 x eps) 2))
5.0ms	(cos (/ (fma 2 x eps) 2))

series238.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (* (* (expm1 (log1p (cos (/ (fma 2 x eps) 2)))) (cos (/ (fma 2 x eps) 2))) (cos (/ (fma 2 x eps) 2))))
25.0ms	(cos (/ (fma 2 x eps) 2))
25.0ms	(cos (/ (fma 2 x eps) 2))
31.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.1s

Counts

54 → 54

Iterations

Iter	Nodes
6	3474
5	1303
4	655
3	312
2	153
1	86
0	45

prune748.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

regimes247.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.6b

bsearch307.0ms

Steps

Iters	Range		Point
10	1.578644681612568e-16	0.0001688282409805197	1.2412047115655244e-08
11	-145.89507053458865	-6.948120050383171e-19	-9.108842191445869e-09

simplify9.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.3s	3376×	body	1280	valid
1.3s	645×	body	2560	valid
895.0ms	1731×	body	640	valid
364.0ms	792×	body	320	valid
144.0ms	1076×	body	80	valid
111.0ms	380×	body	160	valid