Details

sample121.0ms

Algorithm

intervals

Results

53.0ms	98×	body	1280	valid
23.0ms	66×	body	640	valid
19.0ms	17×	body	2560	valid
7.0ms	29×	body	320	valid
2.0ms	34×	body	80	valid
2.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize27.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
4.1b	(sin (+ x eps))

rewrite511.0ms

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:

490.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

series94.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (sin (+ x eps)) (sin x))
38.0ms	(sin (+ x eps))

simplify2.9s

Counts

30 → 30

Iterations

Useful iterations: 4 (447.0ms)

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

prune103.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite150.0ms

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:

55.0ms	(+ (+ x eps) x)
43.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
49.0ms	(cos (/ (+ (+ x eps) x) 2))

series137.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (+ x eps) x)
69.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
43.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.2s

Counts

50 → 50

Iterations

Useful iterations: 4 (2.4s)

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

prune202.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

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)))))
0.6b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite347.0ms

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)))
91.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
138.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
64.0ms	(cos (/ (+ (+ x eps) x) 2))

series255.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
94.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
44.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
37.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.3s

Counts

73 → 73

Iterations

Useful iterations: 4 (1.0s)

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

prune306.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2))))))
0.6b	(* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
3.9b	(cos (/ (+ (+ x eps) x) 2))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-pow1`
36×	`add-sqr-sqrt` `exp-prod`
35×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`log-pow`
18×	`sqrt-prod`
16×	`pow1/2` `pow-prod-up`
12×	`pow-prod-down` `pow-sqr`
9×	`add-exp-log`
8×	`swap-sqr`
6×	`associate-r` `associate-l` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
2×	`pow2` `pow-plus` `rem-log-exp` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

488.0ms	(log (* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2))))))
385.0ms	(* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
89.0ms	(cos (/ (+ (+ x eps) x) 2))
63.0ms	(cos (/ (+ (+ x eps) x) 2))

series198.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(log (* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2))))))
81.0ms	(* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
44.0ms	(cos (/ (+ (+ x eps) x) 2))
47.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.8s

Counts

117 → 117

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	110	2299
1	205	1515
2	447	1282
3	999	1220
4	2405	1174
done	5000	1164

prune426.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes105.0ms

Accuracy

99.4% (0.1b remaining)

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

bsearch157.0ms

Steps

Iters	Range		Point
11	8.666561730544872e-18	9556.682540875734	9.496762876577125e-09
7	-0.006495210018506858	-9.497075983896804e-05	-9.642672794131258e-05

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.6s	3297×	body	1280	valid
1.2s	1868×	body	640	valid
698.0ms	598×	body	2560	valid
172.0ms	799×	body	320	valid
109.0ms	347×	body	160	valid
78.0ms	1091×	body	80	valid