Details

sample211.0ms

Algorithm

intervals

Results

112.0ms	142×	body	1280	valid
49.0ms	34×	body	2560	valid
26.0ms	46×	body	640	valid
11.0ms	28×	body	320	valid
1.0ms	4×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize16.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

17.0ms	(- (cos (+ x eps)) (cos x))
8.0ms	(cos (+ x eps))

series106.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify1.6s

Counts

32 → 32

Iterations

Iter	Nodes
5	3258
4	1330
3	586
2	268
1	135
0	67

prune254.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
3.6b	(sin (/ (+ x (+ x eps)) 2))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

53.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
11.0ms	(+ x (+ x eps))
56.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
31.0ms	(sin (/ (+ x (+ x eps)) 2))

series290.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
42.0ms	(+ x (+ x eps))
103.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
53.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify988.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2396
2	826
1	289
0	123

prune681.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
3.5b	(sin (+ x (* eps 1/2)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `sin-sum` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`insert-posit16` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 30

Calls

2 calls:

51.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
13.0ms	(sin (+ x (* eps 1/2)))

series132.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
48.0ms	(sin (+ x (* eps 1/2)))

simplify3.5s

Counts

36 → 36

Iterations

Iter	Nodes
4	4094
3	1842
2	563
1	190
0	76

prune309.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (cos (* eps 1/2)))
0.2b	(* (cos x) (sin (* eps 1/2)))
0.2b	(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
0.3b	(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`sin-cos-mult` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 86

Calls

4 calls:

18.0ms	(* (sin x) (cos (* eps 1/2)))
18.0ms	(* (cos x) (sin (* eps 1/2)))
87.0ms	(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
95.0ms	(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin x) (cos (* eps 1/2)))
84.0ms	(* (cos x) (sin (* eps 1/2)))
164.0ms	(* (* (sin x) (cos (* eps 1/2))) (* -2 (sin (* eps 1/2))))
76.0ms	(* (* (cos x) (sin (* eps 1/2))) (* -2 (sin (* eps 1/2))))

simplify6.7s

Counts

98 → 98

Iterations

Iter	Nodes
3	8274
2	1655
1	421
0	165

prune926.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes192.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	24
1	24
0	16

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.4s	4532×	body	1280	valid
1.5s	1747×	body	640	valid
1.2s	645×	body	2560	valid
277.0ms	673×	body	320	valid
79.0ms	334×	body	160	valid
8.0ms	69×	body	80	valid