Details

sample214.0ms

Algorithm

intervals

Results

119.0ms	126×	body	1280	valid
35.0ms	69×	body	640	valid
33.0ms	20×	body	2560	valid
11.0ms	25×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	5×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite23.0ms

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:

16.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series105.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(- (cos (+ x eps)) (cos x))
39.0ms	(cos (+ x eps))

simplify1.6s

Counts

32 → 32

Iterations

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

prune337.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

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)))
4.2b	(sin (/ (+ x (+ x eps)) 2))

rewrite201.0ms

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:

88.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
21.0ms	(+ x (+ x eps))
57.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
33.0ms	(sin (/ (+ x (+ x eps)) 2))

series305.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
41.0ms	(+ x (+ x eps))
105.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
52.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify879.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2396
2	826
1	289
0	123

prune806.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
4.3b	(sin (+ x (* eps 1/2)))

rewrite61.0ms

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:

45.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
15.0ms	(sin (+ x (* eps 1/2)))

series110.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
34.0ms	(sin (+ x (* eps 1/2)))

simplify3.5s

Counts

36 → 36

Iterations

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

prune435.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
0.1b	(* (sin x) (cos (* eps 1/2)))
0.2b	(* (cos x) (sin (* eps 1/2)))
0.3b	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

rewrite171.0ms

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:

38.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
17.0ms	(* (sin x) (cos (* eps 1/2)))
17.0ms	(* (cos x) (sin (* eps 1/2)))
97.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
61.0ms	(* (sin x) (cos (* eps 1/2)))
61.0ms	(* (cos x) (sin (* eps 1/2)))
210.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

simplify11.5s

Counts

86 → 86

Iterations

Iter	Nodes
3	8357
2	1834
1	442
0	161

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	18

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.9s	4500×	body	1280	valid
1.7s	633×	body	2560	valid
1.2s	1823×	body	640	valid
270.0ms	685×	body	320	valid
73.0ms	276×	body	160	valid
13.0ms	83×	body	80	valid