Details

sample152.0ms

Algorithm

intervals

Results

78.0ms	113×	body	1280	valid
26.0ms	18×	body	2560	valid
23.0ms	60×	body	640	valid
6.0ms	23×	body	320	valid
3.0ms	32×	body	80	valid
2.0ms	10×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite90.0ms

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:

79.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series83.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (427.0ms)

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

prune105.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.2b	(cos (/ (+ (+ x eps) x) 2))

rewrite124.0ms

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:

53.0ms	(+ (+ x eps) x)
25.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
44.0ms	(cos (/ (+ (+ x eps) x) 2))

series115.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (+ x eps) x)
51.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
37.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.8s

Counts

50 → 50

Iterations

Useful iterations: 4 (2.1s)

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

prune192.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.5b

localize31.0ms

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)
3.2b	(cos (/ (+ (+ x eps) x) 2))

rewrite146.0ms

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:

46.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
7.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
84.0ms	(cos (/ (+ (+ x eps) x) 2))

series207.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
24.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
68.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
41.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.0s

Counts

97 → 97

Iterations

Useful iterations: 3 (1.8s)

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

prune252.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (+ x eps) x) 2)))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
0.5b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
3.2b	(cos (/ (+ (+ x eps) x) 2))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

37.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
68.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
109.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
42.0ms	(cos (/ (+ (+ x eps) x) 2))

series167.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
56.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
27.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.0s

Counts

73 → 73

Iterations

Useful iterations: 4 (686.0ms)

Iter	Nodes	Cost
0	107	1191
1	203	1093
2	461	951
3	871	929
4	1514	927
5	2669	927
done	5001	927

prune192.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

regimes148.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.0b

bsearch105.0ms

Steps

Iters	Range		Point
11	3.560853546224578e-32	4.11075536510938e-11	4.0610401173791624e-11
6	-1.6640733670284383e-05	-3.4900073017642136e-06	-3.523695819775611e-06

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3326×	body	1280	valid
588.0ms	673×	body	2560	valid
458.0ms	1887×	body	640	valid
116.0ms	706×	body	320	valid
66.0ms	1078×	body	80	valid
35.0ms	330×	body	160	valid