Details

sample96.0ms

Algorithm

intervals

Results

39.0ms	97×	body	1280	valid
25.0ms	25×	body	2560	valid
14.0ms	61×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	12×	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:

1.2b	(- (sin (+ x eps)) (sin x))
2.3b	(sin (+ x eps))

rewrite53.0ms

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:

43.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (292.0ms)

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

prune70.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
2.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite83.0ms

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:

25.0ms	(+ (+ x eps) x)
17.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
39.0ms	(cos (/ (+ (+ x eps) x) 2))

series100.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (+ x eps) x)
52.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.8s

Counts

50 → 50

Iterations

Useful iterations: 4 (1.7s)

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

prune125.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
2.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite71.0ms

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:

22.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
3.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
3.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
40.0ms	(cos (/ (+ (+ x eps) x) 2))

series149.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
46.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
28.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
24.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.5s

Counts

97 → 97

Iterations

Useful iterations: 3 (881.0ms)

Iter	Nodes	Cost
0	117	1733
1	247	1447
2	705	1279
3	3810	1245
done	5001	1245

prune211.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (+ x eps) x) 2)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
0.5b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
2.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite201.0ms

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:

36.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
53.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
69.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
41.0ms	(cos (/ (+ (+ x eps) x) 2))

series142.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
51.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
24.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
25.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: 4 (534.0ms)

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

prune183.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes89.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 14.5b

bsearch112.0ms

Steps

Iters	Range		Point
7	1.2981949479042878e-19	3.175736471147199e-18	3.144339914669044e-18
11	-2.8163082396285558e+17	-1.4864914298183363e-09	-8.131893915803983e-09

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	3272×	body	1280	valid
604.0ms	678×	body	2560	valid
474.0ms	1845×	body	640	valid
115.0ms	736×	body	320	valid
62.0ms	1118×	body	80	valid
38.0ms	351×	body	160	valid