Details

sample138.0ms

Algorithm

intervals

Results

66.0ms	126×	body	1280	valid
28.0ms	24×	body	2560	valid
20.0ms	63×	body	640	valid
9.0ms	31×	body	320	valid
2.0ms	10×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize19.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
6.4b	(cos (+ x eps))

rewrite105.0ms

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:

82.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

series135.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(- (cos (+ x eps)) (cos x))
29.0ms	(cos (+ x eps))

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (412.0ms)

Iter	Nodes	Cost
0	65	311
1	135	299
2	266	283
3	540	275
4	1076	273
5	2577	273
done	5001	273

prune178.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

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)))
6.2b	(sin (/ (+ (+ x eps) x) 2))

rewrite357.0ms

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:

133.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
30.0ms	(+ (+ x eps) x)
105.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
87.0ms	(sin (/ (+ (+ x eps) x) 2))

series245.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
44.0ms	(+ (+ x eps) x)
82.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
31.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	119	1098
1	277	1081
2	810	919
3	2388	895
done	5000	889

prune263.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (+ (* 1/2 eps) x)) (* (sin (* 1/2 eps)) -2))
6.2b	(sin (+ (* 1/2 eps) x))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

122.0ms	(* (sin (+ (* 1/2 eps) x)) (* (sin (* 1/2 eps)) -2))
25.0ms	(sin (+ (* 1/2 eps) x))

series129.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(* (sin (+ (* 1/2 eps) x)) (* (sin (* 1/2 eps)) -2))
34.0ms	(sin (+ (* 1/2 eps) x))

simplify9.3s

Counts

32 → 32

Iterations

Useful iterations: 3 (562.0ms)

Iter	Nodes	Cost
0	66	479
1	146	468
2	418	392
3	1338	384
4	2721	384
5	4843	384
done	5000	384

prune143.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

53.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
20.0ms	(* (sin (* 1/2 eps)) (cos x))
31.0ms	(* (cos (* 1/2 eps)) (sin x))
146.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (* (sin (* 1/2 eps)) -2))

series521.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
69.0ms	(* (sin (* 1/2 eps)) (cos x))
89.0ms	(* (cos (* 1/2 eps)) (sin x))
230.0ms	(* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) (* (sin (* 1/2 eps)) -2))

simplify3.8s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	145	1445
1	357	1391
2	1196	1209
3	4524	1203
done	5000	1203

prune365.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	35
1	24	35
done	24	35

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.3s	4423×	body	1280	valid
1.2s	640×	body	2560	valid
996.0ms	1822×	body	640	valid
335.0ms	738×	body	320	valid
77.0ms	299×	body	160	valid
11.0ms	78×	body	80	valid