Details

sample146.0ms

Algorithm

intervals

Results

73.0ms	135×	body	1280	valid
29.0ms	24×	body	2560	valid
21.0ms	61×	body	640	valid
6.0ms	26×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize22.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
3.4b	(cos (+ x eps))

rewrite52.0ms

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:

30.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

series119.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (cos (+ x eps)) (cos x))
29.0ms	(cos (+ x eps))

simplify844.0ms

Counts

30 → 30

Iterations

Useful iterations: done (843.0ms)

Iter	Nodes	Cost
0	65	311
1	135	299
2	339	283
3	1210	275
done	5000	273

prune85.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
0.2b	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
3.5b	(sin (/ (+ (+ x eps) x) 2))

rewrite437.0ms

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-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

35.0ms	(+ (+ x eps) x)
136.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
178.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
85.0ms	(sin (/ (+ (+ x eps) x) 2))

series255.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (+ x eps) x)
102.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
78.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify743.0ms

Counts

72 → 72

Iterations

Useful iterations: done (740.0ms)

Iter	Nodes	Cost
0	119	1098
1	286	1081
2	1163	923
done	5001	895

prune343.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
3.5b	(sin (+ (* 1/2 eps) x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

81.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
32.0ms	(sin (+ (* 1/2 eps) x))

series136.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
42.0ms	(sin (+ (* 1/2 eps) x))

simplify1.0s

Counts

34 → 34

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	72	538
1	185	529
2	977	445
done	5000	441

prune126.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

41.0ms	(+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps))))
37.0ms	(* (sin x) (cos (* 1/2 eps)))
43.0ms	(* (cos x) (sin (* 1/2 eps)))
105.0ms	(* (* -2 (sin (* 1/2 eps))) (+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps)))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps))))
76.0ms	(* (sin x) (cos (* 1/2 eps)))
66.0ms	(* (cos x) (sin (* 1/2 eps)))
219.0ms	(* (* -2 (sin (* 1/2 eps))) (+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps)))))

simplify2.2s

Counts

82 → 82

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	152	1504
1	425	1450
2	2453	1270
done	5001	1268

prune403.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes164.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
1	22	29
done	22	29

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.8s	4454×	body	1280	valid
1.4s	654×	body	2560	valid
781.0ms	1856×	body	640	valid
186.0ms	685×	body	320	valid
54.0ms	271×	body	160	valid
7.0ms	80×	body	80	valid