Details

sample158.0ms

Algorithm

intervals

Results

59.0ms	101×	body	1280	valid
51.0ms	24×	body	2560	valid
24.0ms	66×	body	640	valid
7.0ms	27×	body	320	valid
2.0ms	30×	body	80	valid
1.0ms	8×	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: 37.5b

localize10.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite77.0ms

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:

66.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series75.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify959.0ms

Counts

30 → 30

Iterations

Useful iterations: done (958.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	381	281
3	1453	275
done	5000	271

prune344.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite92.0ms

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:

29.0ms	(+ (+ x eps) x)
16.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms	(cos (/ (+ (+ x eps) x) 2))

series107.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (+ x eps) x)
54.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
29.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify488.0ms

Counts

50 → 50

Iterations

Useful iterations: done (486.0ms)

Iter	Nodes	Cost
0	91	656
1	219	646
2	982	568
done	5000	552

prune222.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

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)))))
0.4b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite245.0ms

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)))
61.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
97.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
49.0ms	(cos (/ (+ (+ x eps) x) 2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
85.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
30.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
33.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.0s

Counts

73 → 73

Iterations

Useful iterations: 3 (890.0ms)

Iter	Nodes	Cost
0	107	1191
1	227	1093
2	807	951
3	4205	931
done	5000	931

prune282.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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)
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite102.0ms

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:

28.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
4.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
6.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
61.0ms	(cos (/ (+ (+ x eps) x) 2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
33.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
56.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
34.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.7s

Counts

97 → 97

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	117	1733
1	299	1463
2	1825	1279
done	5001	1263

prune323.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes168.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.5b

bsearch198.0ms

Steps

Iters	Range		Point
7	2.8927808134808724e-12	4.1843392194405927e-10	4.118793419307952e-10
11	-911936.9907706906	-2.4582005881584278e-17	-9.179827039913243e-09

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	51
1	35	51
done	35	51

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.8s	3325×	body	1280	valid
1.3s	654×	body	2560	valid
732.0ms	1850×	body	640	valid
244.0ms	765×	body	320	valid
119.0ms	1071×	body	80	valid
55.0ms	335×	body	160	valid