Details

sample78.0ms

Algorithm

intervals

Results

32.0ms	56×	body	1280	valid
14.0ms	180×	body	80	valid
12.0ms	37×	body	640	valid
6.0ms	24×	body	320	valid
1.0ms	7×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	52	11
done	52	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (tan B))
0.2b	(/ 1.0 (sin B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

16.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (tan B))
5.0ms	(/ 1.0 (sin B))
18.0ms	(* x (/ 1.0 (tan B)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
36.0ms	(/ 1.0 (tan B))
19.0ms	(/ 1.0 (sin B))
115.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

115 → 115

Iterations

Useful iterations: 3 (741.0ms)

Iter	Nodes	Cost
0	180	1184
1	414	1125
2	1118	1022
3	3390	1017
done	5000	1017

prune314.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
0.1b	(/ x (sin B))
0.2b	(* (* 1.0 (/ x (sin B))) (cos B))
0.2b	(/ 1.0 (sin B))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
17×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
6×	`associate-/r` `associate-/l`
5×	`prod-exp` `cbrt-unprod`
3×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `associate-l` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

19.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
6.0ms	(/ x (sin B))
33.0ms	(* (* 1.0 (/ x (sin B))) (cos B))
6.0ms	(/ 1.0 (sin B))

series285.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
53.0ms	(/ x (sin B))
105.0ms	(* (* 1.0 (/ x (sin B))) (cos B))
20.0ms	(/ 1.0 (sin B))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	173	1214
1	406	1164
2	1363	1019
done	5000	1012

prune266.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ (* 1.0 x) (/ (sin B) (cos B)))) (/ 1.0 (sin B)))
0.1b	(/ (* 1.0 x) (/ (sin B) (cos B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (sin B) (cos B))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
38×	`*-un-lft-identity`
34×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
8×	`cbrt-undiv` `div-exp` `add-log-exp`
7×	`associate-/l*`
5×	`div-inv`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `quot-tan` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `associate-/r/` `flip-+` `distribute-neg-frac`

Counts

4 → 117

Calls

4 calls:

77.0ms	(+ (- (/ (* 1.0 x) (/ (sin B) (cos B)))) (/ 1.0 (sin B)))
15.0ms	(/ (* 1.0 x) (/ (sin B) (cos B)))
5.0ms	(/ 1.0 (sin B))
9.0ms	(/ (sin B) (cos B))

series255.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (- (/ (* 1.0 x) (/ (sin B) (cos B)))) (/ 1.0 (sin B)))
108.0ms	(/ (* 1.0 x) (/ (sin B) (cos B)))
19.0ms	(/ 1.0 (sin B))
20.0ms	(/ (sin B) (cos B))

simplify1.1s

Counts

129 → 129

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	213	1671
1	503	1589
2	1758	1425
done	5001	1361

prune332.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1.0 (sin B)) (- (* x (cos B)) 1))
0.2b	(* x (cos B))
0.2b	(/ 1.0 (sin B))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-l`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `sub-neg` `flip3--` `distribute-lft-in` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

3 → 85

Calls

3 calls:

47.0ms	(* (/ 1.0 (sin B)) (- (* x (cos B)) 1))
11.0ms	(* x (cos B))
6.0ms	(/ 1.0 (sin B))

series137.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(* (/ 1.0 (sin B)) (- (* x (cos B)) 1))
36.0ms	(* x (cos B))
23.0ms	(/ 1.0 (sin B))

simplify2.9s

Counts

94 → 94

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	152	1065
1	359	1016
2	1107	914
3	4389	911
done	5000	911

prune215.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes64.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	16	12
2	18	12
3	24	12
done	24	12

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1742×	body	1280	valid
488.0ms	1409×	body	640	valid
382.0ms	4896×	body	80	valid
178.0ms	744×	body	320	valid
61.0ms	340×	body	160	valid