Details

sample207.0ms

Algorithm

intervals

Results

126.0ms	148×	body	1280	valid
32.0ms	21×	body	2560	valid
29.0ms	55×	body	640	valid
6.0ms	19×	body	320	valid
3.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	24
2	24
1	21
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize40.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite39.0ms

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:

21.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(- (cos (+ x eps)) (cos x))
28.0ms	(cos (+ x eps))

simplify1.4s

Counts

32 → 32

Iterations

Iter	Nodes
5	3068
4	1498
3	788
2	425
1	261
0	67

prune295.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

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)))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite205.0ms

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:

80.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
12.0ms	(+ x (+ x eps))
76.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

series262.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
29.0ms	(+ x (+ x eps))
96.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
3	2791
2	1129
1	511
0	123

prune812.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
3.2b	(sin (+ x (* eps 1/2)))

rewrite73.0ms

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:

57.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
15.0ms	(sin (+ x (* eps 1/2)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
33.0ms	(sin (+ x (* eps 1/2)))

simplify2.7s

Counts

36 → 36

Iterations

Iter	Nodes
4	3621
3	1883
2	734
1	327
0	76

prune452.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
0.1b	(* (cos x) (sin (* eps 1/2)))
0.1b	(* (sin x) (cos (* eps 1/2)))
0.3b	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

25.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
19.0ms	(* (cos x) (sin (* eps 1/2)))
18.0ms	(* (sin x) (cos (* eps 1/2)))
110.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
86.0ms	(* (cos x) (sin (* eps 1/2)))
61.0ms	(* (sin x) (cos (* eps 1/2)))
197.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

simplify639.0ms

Counts

86 → 86

Iterations

Iter	Nodes
2	2122
1	729
0	161

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	20
1	20
0	14

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.9s	4421×	body	1280	valid
1.4s	1867×	body	640	valid
1.2s	643×	body	2560	valid
726.0ms	706×	body	320	valid
72.0ms	280×	body	160	valid
11.0ms	83×	body	80	valid