Details

sample89.0ms

Algorithm

intervals

Results

40.0ms	96×	body	1280	valid
20.0ms	22×	body	2560	valid
13.0ms	57×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	39×	body	80	valid
2.0ms	17×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 34.0b

localize9.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ 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` `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:

24.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

series58.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.4s

Counts

30 → 30

Iterations

Useful iterations: 4 (233.0ms)

Iter	Nodes	Cost
0	64	309
1	134	295
2	295	281
3	543	275
4	1107	271
5	2499	271
done	5000	271

prune73.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite45.0ms

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:

13.0ms	(+ (+ x eps) x)
6.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
24.0ms	(cos (/ (+ (+ x eps) x) 2))

series95.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
49.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
24.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.8s

Counts

50 → 50

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	91	656
1	212	646
2	526	566
3	1350	556
4	4394	548
done	5001	548

prune130.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite41.0ms

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:

12.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
1.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
1.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
23.0ms	(cos (/ (+ (+ x eps) x) 2))

series138.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
22.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
48.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
23.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.2s

Counts

97 → 97

Iterations

Useful iterations: 3 (707.0ms)

Iter	Nodes	Cost
0	117	1733
1	254	1447
2	735	1279
3	3628	1259
done	5001	1259

prune236.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
0.5b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
3.9b	(cos (/ (+ (+ x eps) x) 2))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite46.0ms

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 (pow (cos (/ (+ (+ x eps) x) 2)) 2))
1.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
23.0ms	(cos (/ (+ (+ x eps) x) 2))
20.0ms	(cos (/ (+ (+ x eps) x) 2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
77.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
22.0ms	(cos (/ (+ (+ x eps) x) 2))
22.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.0s

Counts

53 → 53

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	71	779
1	147	704
2	299	630
3	597	608
4	1948	608
done	5001	608

prune168.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

regimes112.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.2b

bsearch123.0ms

Steps

Iters	Range		Point
10	9.278264258908537e-20	9.143643357499823e-08	1.1905404803477009e-08
9	-1.0255030941766934e-06	-9.091202463712598e-16	-8.781839081277773e-09

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3282×	body	1280	valid
604.0ms	686×	body	2560	valid
452.0ms	1818×	body	640	valid
123.0ms	736×	body	320	valid
54.0ms	1121×	body	80	valid
37.0ms	357×	body	160	valid