Details

sample147.0ms

Algorithm

intervals

Results

70.0ms	103×	body	1280	valid
25.0ms	19×	body	2560	valid
24.0ms	55×	body	640	valid
7.0ms	26×	body	320	valid
4.0ms	44×	body	80	valid
2.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize17.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (sin (+ x eps)) (sin x))
3.4b	(sin (+ 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` `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:

50.0ms	(- (sin (+ x eps)) (sin x))
54.0ms	(sin (+ x eps))

series70.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify2.6s

Counts

30 → 30

Iterations

Useful iterations: 4 (338.0ms)

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

prune115.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
0.2b	(/ (+ (+ x eps) x) 2)
3.4b	(cos (/ (+ (+ x eps) x) 2))

rewrite238.0ms

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-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `sum-log`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `sin-cos-mult` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

51.0ms	(+ (+ x eps) x)
31.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
95.0ms	(/ (+ (+ x eps) x) 2)
57.0ms	(cos (/ (+ (+ x eps) x) 2))

series188.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (+ x eps) x)
66.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
52.0ms	(/ (+ (+ x eps) x) 2)
37.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.0s

Counts

90 → 90

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	133	1132
1	298	1099
2	769	995
3	1942	971
done	5000	959

prune270.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
3.4b	(cos (/ (+ (+ x eps) x) 2))
3.4b	(cos (/ (+ (+ x eps) x) 2))
3.4b	(cos (/ (+ (+ x eps) x) 2))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 31

Calls

4 calls:

11.0ms	(cbrt (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
83.0ms	(cos (/ (+ (+ x eps) x) 2))
63.0ms	(cos (/ (+ (+ x eps) x) 2))
59.0ms	(cos (/ (+ (+ x eps) x) 2))

series261.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
34.0ms	(cos (/ (+ (+ x eps) x) 2))
32.0ms	(cos (/ (+ (+ x eps) x) 2))
44.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.0s

Counts

43 → 43

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	65	617
1	133	609
2	240	527
3	533	497
4	1538	489
done	5000	488

prune235.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2))))))
3.4b	(cos (/ (+ (+ x eps) x) 2))
3.4b	(cos (/ (+ (+ x eps) x) 2))
3.4b	(cos (/ (+ (+ x eps) x) 2))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 30

Calls

4 calls:

6.0ms	(cbrt (* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2))))))
52.0ms	(cos (/ (+ (+ x eps) x) 2))
71.0ms	(cos (/ (+ (+ x eps) x) 2))
46.0ms	(cos (/ (+ (+ x eps) x) 2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2))))))
35.0ms	(cos (/ (+ (+ x eps) x) 2))
27.0ms	(cos (/ (+ (+ x eps) x) 2))
28.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.5s

Counts

42 → 42

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	60	611
1	124	581
2	230	499
3	516	469
4	1514	461
done	5000	460

prune238.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes99.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.1b

bsearch145.0ms

Steps

Iters	Range		Point
8	9.073269354155488e-21	1.3273336497419229e-17	1.3130033279220329e-17
9	-0.002338049553438653	-4.347782938444816e-12	-1.1565737311297234e-08

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	3371×	body	1280	valid
802.0ms	611×	body	2560	valid
674.0ms	1842×	body	640	valid
183.0ms	720×	body	320	valid
111.0ms	1114×	body	80	valid
83.0ms	342×	body	160	valid