Details

sample387.0ms

Algorithm

intervals

Results

155.0ms	142×	body	1280	valid
60.0ms	69×	body	640	valid
28.0ms	16×	body	2560	valid
9.0ms	11×	body	160	valid
6.0ms	17×	body	320	valid
0.0ms	1×	body	80	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize34.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

36.0ms	(- (cos (+ x eps)) (cos x))
171.0ms	(cos (+ x eps))

series355.0ms

Counts

2 → 6

Calls

2 calls:

197.0ms	(- (cos (+ x eps)) (cos x))
158.0ms	(cos (+ x eps))

simplify11.8s

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
5	3832
4	1446
3	647
2	282
1	135
0	65

prune762.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
0.0b	(+ x (+ eps x))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
4.7b	(sin (/ (+ x (+ eps x)) 2))

rewrite471.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

166.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
43.0ms	(+ x (+ eps x))
176.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
82.0ms	(sin (/ (+ x (+ eps x)) 2))

series495.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
85.0ms	(+ x (+ eps x))
131.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
92.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify9.8s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	3267
2	809
1	285
0	119

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (+ x (/ eps 2))) (* (sin (/ eps 2)) -2))
4.6b	(sin (+ x (/ eps 2)))

rewrite464.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

403.0ms	(* (sin (+ x (/ eps 2))) (* (sin (/ eps 2)) -2))
59.0ms	(sin (+ x (/ eps 2)))

series232.0ms

Counts

2 → 6

Calls

2 calls:

170.0ms	(* (sin (+ x (/ eps 2))) (* (sin (/ eps 2)) -2))
61.0ms	(sin (+ x (/ eps 2)))

simplify9.7s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
3	1154
2	408
1	154
0	67

prune613.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))
0.1b	(* (cos x) (sin (/ eps 2)))
0.2b	(* (sin x) (cos (/ eps 2)))
0.3b	(* (+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2)))) (* (sin (/ eps 2)) -2))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`*-commutative`
2×	`flip3-+` `associate-*l/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `sin-cos-mult`

Counts

4 → 68

Calls

4 calls:

72.0ms	(+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))
38.0ms	(* (cos x) (sin (/ eps 2)))
28.0ms	(* (sin x) (cos (/ eps 2)))
173.0ms	(* (+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2)))) (* (sin (/ eps 2)) -2))

series2.0s

Counts

4 → 12

Calls

4 calls:

485.0ms	(+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2))))
488.0ms	(* (cos x) (sin (/ eps 2)))
192.0ms	(* (sin x) (cos (/ eps 2)))
835.0ms	(* (+ (* (sin x) (cos (/ eps 2))) (* (cos x) (sin (/ eps 2)))) (* (sin (/ eps 2)) -2))

simplify14.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
3	4923
2	1196
1	380
0	148

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes816.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end6.0ms

sample37.1s

Algorithm

intervals

Results

26.3s	4443×	body	1280	valid
4.9s	1849×	body	640	valid
4.5s	646×	body	2560	valid
512.0ms	691×	body	320	valid
111.0ms	293×	body	160	valid
22.0ms	78×	body	80	valid