Details

sample170.0ms

Algorithm

intervals

Results

88.0ms	107×	body	1280	valid
25.0ms	17×	body	2560	valid
23.0ms	49×	body	640	valid
8.0ms	24×	body	320	valid
5.0ms	19×	body	160	valid
4.0ms	40×	body	80	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

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize12.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ x eps))

rewrite101.0ms

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:

89.0ms	(- (sin (+ x eps)) (sin x))
11.0ms	(sin (+ x eps))

series99.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (sin (+ x eps)) (sin x))
35.0ms	(sin (+ x eps))

simplify1.1s

Counts

30 → 30

Iterations

Useful iterations: done (1.1s)

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

prune121.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
4.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite145.0ms

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:

44.0ms	(+ (+ x eps) x)
34.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
66.0ms	(cos (/ (+ (+ x eps) x) 2))

series136.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ x eps) x)
75.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify608.0ms

Counts

50 → 50

Iterations

Useful iterations: done (606.0ms)

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

prune169.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

localize24.0ms

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))))
4.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite290.0ms

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:

50.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
71.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
96.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
72.0ms	(cos (/ (+ (+ x eps) x) 2))

series201.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
63.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
31.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
35.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.3s

Counts

73 → 73

Iterations

Useful iterations: 3 (907.0ms)

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

prune344.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (exp (cos (/ (+ (+ x eps) x) 2))) 3))
0.4b	(log (cbrt (pow (exp (cos (/ (+ (+ x eps) x) 2))) 3)))
0.8b	(pow (exp (cos (/ (+ (+ x eps) x) 2))) 3)
4.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
9×	`unpow-prod-down` `cube-prod`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow-pow` `add-log-exp`
3×	`cube-mult` `pow-unpow` `exp-prod` `unpow3` `sqr-pow`
2×	`pow1/3` `log-pow`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

80.0ms	(cbrt (pow (exp (cos (/ (+ (+ x eps) x) 2))) 3))
152.0ms	(log (cbrt (pow (exp (cos (/ (+ (+ x eps) x) 2))) 3)))
92.0ms	(pow (exp (cos (/ (+ (+ x eps) x) 2))) 3)
52.0ms	(cos (/ (+ (+ x eps) x) 2))

series267.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(cbrt (pow (exp (cos (/ (+ (+ x eps) x) 2))) 3))
48.0ms	(log (cbrt (pow (exp (cos (/ (+ (+ x eps) x) 2))) 3)))
119.0ms	(pow (exp (cos (/ (+ (+ x eps) x) 2))) 3)
28.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.1s

Counts

91 → 91

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	112	1707
1	279	1411
2	1128	1217
done	5000	1187

prune353.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.5b

regimes177.0ms

Accuracy

96.5% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 14.7b

bsearch174.0ms

Steps

Iters	Range		Point
7	1.8363952280958253e-30	3.491579857798755e-29	3.449975298893777e-29
8	-1.3483780562815135e-05	-8.792466138214151e-10	-8.703827292805687e-09

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample7.0s

Algorithm

intervals

Results

4.0s	3380×	body	1280	valid
1.0s	614×	body	2560	valid
910.0ms	1794×	body	640	valid
489.0ms	741×	body	320	valid
165.0ms	1150×	body	80	valid
68.0ms	321×	body	160	valid