Details

sample179.0ms

Algorithm

intervals

Results

109.0ms	147×	body	1280	valid
26.0ms	20×	body	2560	valid
19.0ms	55×	body	640	valid
5.0ms	17×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	7×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	202
1	9	202
2	10	202
done	10	202

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize26.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

22.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

series164.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (cos (+ x eps)) (cos x))
71.0ms	(cos (+ x eps))

simplify1.0s

Counts

30 → 30

Iterations

Useful iterations: done (998.0ms)

Iter	Nodes	Cost
0	65	8505
1	135	7661
2	337	7661
3	1232	7581
done	5001	7501

prune223.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(/ (+ (+ x eps) x) 2)
0.3b	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
2.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

32.0ms	(+ (+ x eps) x)
96.0ms	(/ (+ (+ x eps) x) 2)
121.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
64.0ms	(sin (/ (+ (+ x eps) x) 2))

series246.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (+ x eps) x)
40.0ms	(/ (+ (+ x eps) x) 2)
121.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
56.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.0s

Counts

90 → 90

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	132	23551
1	300	22011
2	1202	21971
done	5001	21567

prune519.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize91.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
2.4b	(sin (/ (+ (+ x eps) x) 2))
2.4b	(sin (/ (+ (+ x eps) x) 2))
2.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

27.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
43.0ms	(sin (/ (+ (+ x eps) x) 2))
45.0ms	(sin (/ (+ (+ x eps) x) 2))
44.0ms	(sin (/ (+ (+ x eps) x) 2))

series248.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
49.0ms	(sin (/ (+ (+ x eps) x) 2))
40.0ms	(sin (/ (+ (+ x eps) x) 2))
33.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify991.0ms

Counts

44 → 44

Iterations

Useful iterations: done (985.0ms)

Iter	Nodes	Cost
0	57	13386
1	119	12481
2	301	12481
3	1048	11993
done	5000	11682

prune387.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
2.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
51.0ms	(sin (/ (+ (+ x eps) x) 2))

series550.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (sin (/ eps 2)))
172.0ms	(cbrt (sin (/ eps 2)))
175.0ms	(cbrt (sin (/ eps 2)))
41.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.2s

Counts

52 → 52

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	60	16408
1	121	14225
2	295	14225
3	1231	13543
done	5001	12910

prune404.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

regimes679.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch190.0ms

Steps

Iters	Range		Point
10	7.42116589675916e-09	160.65039477392645	0.00014597753908590782
9	-3322970397.4786234	-6367.3348759504115	-6443.306290177518

simplify16.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	26	1026
1	35	1026
done	35	1026

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.2s	4435×	body	1280	valid
1.2s	1874×	body	640	valid
997.0ms	637×	body	2560	valid
647.0ms	665×	body	320	valid
114.0ms	307×	body	160	valid
8.0ms	82×	body	80	valid