Details

sample169.0ms

Algorithm

intervals

Results

66.0ms	143×	body	1280	valid
63.0ms	20×	body	2560	valid
17.0ms	56×	body	640	valid
6.0ms	24×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite29.0ms

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:

16.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series108.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- (cos (+ x eps)) (cos x))
25.0ms	(cos (+ x eps))

simplify868.0ms

Counts

30 → 30

Iterations

Useful iterations: done (867.0ms)

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

prune136.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

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)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite385.0ms

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:

115.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
54.0ms	(+ (+ x eps) x)
149.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
64.0ms	(sin (/ (+ (+ x eps) x) 2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
31.0ms	(+ (+ x eps) x)
65.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify720.0ms

Counts

72 → 72

Iterations

Useful iterations: done (718.0ms)

Iter	Nodes	Cost
0	119	1098
1	284	1081
2	1056	923
done	5001	895

prune303.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
4.2b	(sin (+ (* 1/2 eps) x))

rewrite113.0ms

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:

90.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
22.0ms	(sin (+ (* 1/2 eps) x))

series136.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
43.0ms	(sin (+ (* 1/2 eps) x))

simplify855.0ms

Counts

34 → 34

Iterations

Useful iterations: done (854.0ms)

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

prune120.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

33.0ms	(* (cos (* 1/2 eps)) (sin x))
20.0ms	(* (sin (* 1/2 eps)) (cos x))
107.0ms	(* (* (cos (* 1/2 eps)) (sin x)) (* -2 (sin (* 1/2 eps))))
126.0ms	(* (* (sin (* 1/2 eps)) (cos x)) (* -2 (sin (* 1/2 eps))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (cos (* 1/2 eps)) (sin x))
65.0ms	(* (sin (* 1/2 eps)) (cos x))
114.0ms	(* (* (cos (* 1/2 eps)) (sin x)) (* -2 (sin (* 1/2 eps))))
84.0ms	(* (* (sin (* 1/2 eps)) (cos x)) (* -2 (sin (* 1/2 eps))))

simplify1.6s

Counts

94 → 94

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	155	1477
1	412	1413
2	2143	1068
done	5000	1052

prune348.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes148.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	24	29
done	24	29

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.6s	4426×	body	1280	valid
2.1s	609×	body	2560	valid
874.0ms	1880×	body	640	valid
222.0ms	697×	body	320	valid
103.0ms	312×	body	160	valid
7.0ms	76×	body	80	valid