Details

sample133.0ms

Algorithm

intervals

Results

64.0ms	60×	body	1280	valid
25.0ms	47×	body	640	valid
17.0ms	138×	body	80	valid
11.0ms	28×	body	320	valid
3.0ms	13×	body	160	valid

simplify38.0ms

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

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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 (sin B))
9.0ms	(/ 1.0 (tan B))
27.0ms	(* x (/ 1.0 (tan B)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
55.0ms	(/ 1.0 (tan B))
161.0ms	(* x (/ 1.0 (tan B)))

simplify2.0s

Counts

115 → 115

Iterations

Useful iterations: 3 (953.0ms)

Iter	Nodes	Cost
0	180	1184
1	414	1125
2	1121	1022
3	3390	1017
done	5000	1017

prune468.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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:

22.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
11.0ms	(/ x (sin B))
11.0ms	(/ 1.0 (sin B))
48.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

series391.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
70.0ms	(/ x (sin B))
21.0ms	(/ 1.0 (sin B))
151.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	173	1214
1	406	1164
2	1367	1019
done	5000	1012

prune407.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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`
4×	`associate-*r/`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `associate-r` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

31.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
10.0ms	(/ (cos B) (sin B))
26.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
40.0ms	(/ 1.0 (sin B))
39.0ms	(/ (cos B) (sin B))
145.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	174	1253
1	405	1205
2	1272	1056
done	5000	1049

prune364.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* 1 (/ (* x 1.0) (/ (sin B) (cos B))))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (sin B) (cos B))
0.2b	(/ (* x 1.0) (/ (sin B) (cos B)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
37×	`*-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-+` `associate-*r/` `neg-log` `frac-add` `associate-/r/` `flip-+` `distribute-neg-frac`

Counts

4 → 117

Calls

4 calls:

20.0ms	(+ (- (* 1 (/ (* x 1.0) (/ (sin B) (cos B))))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
14.0ms	(/ (sin B) (cos B))
15.0ms	(/ (* x 1.0) (/ (sin B) (cos B)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (- (* 1 (/ (* x 1.0) (/ (sin B) (cos B))))) (/ 1.0 (sin B)))
47.0ms	(/ 1.0 (sin B))
43.0ms	(/ (sin B) (cos B))
194.0ms	(/ (* x 1.0) (/ (sin B) (cos B)))

simplify1.5s

Counts

129 → 129

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	221	1715
1	520	1591
2	1856	1425
done	5000	1415

prune564.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	26	15
3	28	15
done	28	15

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.5s	1713×	body	1280	valid
1.7s	1334×	body	640	valid
1.1s	4910×	body	80	valid
508.0ms	790×	body	320	valid
281.0ms	383×	body	160	valid