Details

sample248.0ms

Algorithm

intervals

Results

148.0ms	151×	body	1280	valid
47.0ms	27×	body	2560	valid
32.0ms	54×	body	640	valid
7.0ms	17×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize61.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (cos (+ x eps)) (cos x))
2.7b	(cos (+ x eps))

rewrite43.0ms

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` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

23.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

series126.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(- (cos (+ x eps)) (cos x))
29.0ms	(cos (+ x eps))

simplify1.7s

Counts

48 → 48

Iterations

Iter	Nodes
4	2971
3	1064
2	408
1	200
0	93

prune501.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.4b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

37.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
15.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series241.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
99.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
44.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.9s

Counts

63 → 63

Iterations

Iter	Nodes
4	5559
3	1699
2	588
1	224
0	102

prune756.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `*-commutative`

Counts

2 → 31

Calls

2 calls:

48.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series136.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
48.0ms	(sin (/ (fma 2 x eps) 2))

simplify3.0s

Counts

37 → 37

Iterations

Iter	Nodes
4	4297
3	1550
2	472
1	171
0	73

prune406.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))
3.0b	(sin (/ (fma 2 x eps) 2))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))
3.0ms	(sin (/ (fma 2 x eps) 2))
3.0ms	(sin (/ (fma 2 x eps) 2))

series260.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
51.0ms	(sin (/ (fma 2 x eps) 2))
57.0ms	(sin (/ (fma 2 x eps) 2))
45.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.4s

Counts

56 → 56

Iterations

Iter	Nodes
5	4254
4	1496
3	584
2	249
1	115
0	60

prune781.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.4b

regimes269.0ms

Accuracy

96.9% (0.5b remaining)

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

bsearch276.0ms

Steps

Iters	Range		Point
9	6.506845775939919e-17	2.0554446490307063e-08	2.0143977468052977e-08
10	-8.26555774309129e+15	-0.09702975014721212	-0.0987473663124097

simplify5.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.3s	4397×	body	1280	valid
1.6s	695×	body	2560	valid
1.3s	1915×	body	640	valid
272.0ms	655×	body	320	valid
135.0ms	266×	body	160	valid
9.0ms	72×	body	80	valid