Details

sample324.0ms

Algorithm

intervals

Results

31.0ms	55×	body	1280	valid
15.0ms	45×	body	640	valid
13.0ms	165×	body	80	valid
5.0ms	20×	body	320	valid
3.0ms	10×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	32	11
3	44	11
4	55	11
5	60	11
6	62	11
done	62	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:

9.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
11.0ms	(* x (/ 1.0 (tan B)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
128.0ms	(* x (/ 1.0 (tan B)))

simplify1.8s

Counts

129 → 129

Iterations

Useful iterations: 3 (923.0ms)

Iter	Nodes	Cost
0	188	1244
1	438	1180
2	1144	1075
3	3837	1067
done	5001	1067

prune368.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

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:

35.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series241.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
109.0ms	(/ (* x 1.0) (tan B))

simplify2.0s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	150	887
1	350	843
2	989	755
3	3983	747
done	5001	747

prune277.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.1b	(fma (- (/ x 1)) (/ 1.0 (tan B)) (/ 1.0 (sin B)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
0.0ms	(fma (- (/ x 1)) (/ 1.0 (tan B)) (/ 1.0 (sin B)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
99.0ms	(fma (- (/ x 1)) (/ 1.0 (tan B)) (/ 1.0 (sin B)))

simplify1.8s

Counts

78 → 78

Iterations

Useful iterations: 4 (878.0ms)

Iter	Nodes	Cost
0	131	756
1	250	704
2	522	644
3	1196	644
4	3008	636
done	5001	636

prune245.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (sin B))
14.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
8.0ms	(* x (/ 1.0 (sin B)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (sin B))
103.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
59.0ms	(* x (/ 1.0 (sin B)))

simplify2.7s

Counts

127 → 127

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	140	1194
1	325	1146
2	1030	1008
3	4651	1002
done	5000	1002

prune314.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	17	15
2	25	15
3	27	15
done	27	15

end0.0ms

sample2.5s

Algorithm

intervals

Results

998.0ms	1700×	body	1280	valid
677.0ms	1461×	body	640	valid
378.0ms	4889×	body	80	valid
171.0ms	725×	body	320	valid
61.0ms	368×	body	160	valid