Details

sample455.0ms

Algorithm

intervals

Results

168.0ms	50×	body	1280	valid
137.0ms	160×	body	80	valid
48.0ms	50×	body	640	valid
18.0ms	25×	body	320	valid
3.0ms	7×	body	160	valid

simplify151.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	60	11
6	62	11
done	62	11

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize66.0ms

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))
0.2b	(* x (/ 1.0 (tan B)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

75.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
15.0ms	(/ 1.0 (tan B))
72.0ms	(* x (/ 1.0 (tan B)))

series794.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
142.0ms	(/ 1.0 (sin B))
147.0ms	(/ 1.0 (tan B))
194.0ms	(* x (/ 1.0 (tan B)))

simplify1.1s

Counts

129 → 129

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	188	1244
1	462	1184
2	1710	1083
done	5000	1074

prune602.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

71.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
22.0ms	(/ (* x 1.0) (tan B))
11.0ms	(/ 1.0 (sin B))

series343.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
157.0ms	(/ (* x 1.0) (tan B))
38.0ms	(/ 1.0 (sin B))

simplify1.1s

Counts

100 → 100

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	150	887
1	370	843
2	1548	761
done	5000	756

prune506.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`distribute-rgt-neg-in` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

16.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
25.0ms	(* x (cos B))
12.0ms	(/ 1.0 (sin B))
25.0ms	(/ (* x (cos B)) (sin B))

series411.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
57.0ms	(* x (cos B))
38.0ms	(/ 1.0 (sin B))
147.0ms	(/ (* x (cos B)) (sin B))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	162	1113
1	394	1066
2	1605	956
done	5000	943

prune471.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`prod-exp` `cbrt-unprod` `fma-udef`

Counts

3 → 62

Calls

3 calls:

0.0ms	(fma (/ (* x 1.0) (sin B)) (- (cos B)) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (sin B))

series253.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(fma (/ (* x 1.0) (sin B)) (- (cos B)) (/ 1.0 (sin B)))
24.0ms	(/ 1.0 (sin B))
84.0ms	(/ (* x 1.0) (sin B))

simplify899.0ms

Counts

71 → 71

Iterations

Useful iterations: done (895.0ms)

Iter	Nodes	Cost
0	120	737
1	279	713
2	1193	637
done	5000	635

prune301.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes133.0ms

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	22	15
3	28	15
done	28	15

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.5s	1418×	body	640	valid
2.4s	1737×	body	1280	valid
817.0ms	5000×	body	80	valid
362.0ms	689×	body	320	valid
112.0ms	363×	body	160	valid