Details

sample127.0ms

Algorithm

intervals

Results

69.0ms	140×	body	1280	valid
18.0ms	17×	body	2560	valid
17.0ms	56×	body	640	valid
6.0ms	29×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	2×	body	80	valid

simplify6.0ms

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: 42.3b

localize43.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (cos (+ x eps)) (cos x))
3.9b	(cos (+ x eps))

rewrite48.0ms

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:

26.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

series127.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (cos (+ x eps)) (cos x))
37.0ms	(cos (+ x eps))

simplify686.0ms

Counts

30 → 30

Iterations

Useful iterations: done (685.0ms)

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

prune140.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

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)))
4.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite301.0ms

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:

125.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
29.0ms	(+ (+ x eps) x)
99.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
45.0ms	(sin (/ (+ (+ x eps) x) 2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
29.0ms	(+ (+ x eps) x)
83.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
57.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify657.0ms

Counts

72 → 72

Iterations

Useful iterations: done (654.0ms)

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

prune323.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
3.9b	(sin (+ (* 1/2 eps) x))

rewrite108.0ms

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:

86.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
20.0ms	(sin (+ (* 1/2 eps) x))

series113.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)))
30.0ms	(sin (+ (* 1/2 eps) x))

simplify869.0ms

Counts

34 → 34

Iterations

Useful iterations: done (868.0ms)

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

prune173.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite207.0ms

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:

44.0ms	(+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps))))
22.0ms	(* (cos x) (sin (* 1/2 eps)))
25.0ms	(* (sin x) (cos (* 1/2 eps)))
113.0ms	(* (* -2 (sin (* 1/2 eps))) (+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps)))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps))))
77.0ms	(* (cos x) (sin (* 1/2 eps)))
70.0ms	(* (sin x) (cos (* 1/2 eps)))
236.0ms	(* (* -2 (sin (* 1/2 eps))) (+ (* (cos x) (sin (* 1/2 eps))) (* (sin x) (cos (* 1/2 eps)))))

simplify1.8s

Counts

82 → 82

Iterations

Useful iterations: 2 (449.0ms)

Iter	Nodes	Cost
0	152	1504
1	425	1450
2	2439	1268
done	5001	1268

prune414.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes170.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	24	31
done	24	31

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.8s	4535×	body	1280	valid
1.8s	1834×	body	640	valid
931.0ms	614×	body	2560	valid
195.0ms	662×	body	320	valid
108.0ms	269×	body	160	valid
10.0ms	86×	body	80	valid