Details

sample152.0ms

Algorithm

intervals

Results

75.0ms	106×	body	1280	valid
26.0ms	58×	body	640	valid
23.0ms	16×	body	2560	valid
8.0ms	25×	body	320	valid
3.0ms	36×	body	80	valid
3.0ms	15×	body	160	valid

simplify7.0ms

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: 38.0b

localize42.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

49.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series84.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (sin (+ x eps)) (sin x))
31.0ms	(sin (+ x eps))

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (504.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	284	281
3	572	275
4	1162	271
5	2763	271
done	5000	271

prune99.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.6b	(cos (/ (+ (+ x eps) x) 2))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

32.0ms	(+ (+ x eps) x)
19.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
41.0ms	(cos (/ (+ (+ x eps) x) 2))

series160.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (+ x eps) x)
91.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.8s

Counts

50 → 50

Iterations

Useful iterations: 4 (2.3s)

Iter	Nodes	Cost
0	91	656
1	213	646
2	546	566
3	1366	548
4	4627	540
done	5000	540

prune169.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.4b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.6b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
3.6b	(cos (/ (+ (+ x eps) x) 2))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

41.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
3.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
3.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
51.0ms	(cos (/ (+ (+ x eps) x) 2))

series212.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
26.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
67.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
45.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.7s

Counts

97 → 97

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	117	1733
1	247	1447
2	705	1279
3	3806	1245
done	5000	1245

prune338.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
3.6b	(cos (/ (+ (+ x eps) x) 2))
3.6b	(cos (/ (+ (+ x eps) x) 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
2×	`pow1/3`
1×	`unpow2` `sqr-pow`

Counts

4 → 41

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
2.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
43.0ms	(cos (/ (+ (+ x eps) x) 2))
53.0ms	(cos (/ (+ (+ x eps) x) 2))

series281.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
123.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
27.0ms	(cos (/ (+ (+ x eps) x) 2))
34.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

53 → 53

Iterations

Useful iterations: 3 (158.0ms)

Iter	Nodes	Cost
0	71	779
1	148	704
2	277	630
3	580	608
4	2149	608
done	5001	608

prune189.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes109.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.3b

bsearch127.0ms

Steps

Iters	Range		Point
10	7.973842016810099e-17	7.806085722401822e-05	8.837665134522453e-09
7	-0.22637101271021068	-0.008005822963963436	-0.00815188689103541

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	51
1	35	38
done	35	38

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3220×	body	1280	valid
1.1s	1919×	body	640	valid
709.0ms	633×	body	2560	valid
200.0ms	735×	body	320	valid
127.0ms	354×	body	160	valid
123.0ms	1139×	body	80	valid