Details

sample80.0ms

Algorithm

intervals

Results

33.0ms	55×	body	1280	valid
16.0ms	45×	body	640	valid
13.0ms	165×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

prune5.0ms

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

rewrite29.0ms

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:

12.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
2.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
114.0ms	(* x (/ 1.0 (tan B)))

simplify1.7s

Counts

129 → 129

Iterations

Useful iterations: 3 (895.0ms)

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

prune372.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite43.0ms

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:

31.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series242.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (sin B))
109.0ms	(/ (* x 1.0) (tan B))

simplify1.9s

Counts

100 → 100

Iterations

Useful iterations: 3 (947.0ms)

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

prune274.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1 (tan B))
0.1b	(fma (- (* x 1.0)) (/ 1 (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`
9×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`pow1`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
1×	`tan-quot` `rec-exp` `pow-flip` `1-exp` `associate-/r/` `fma-udef` `inv-pow`

Counts

3 → 73

Calls

3 calls:

2.0ms	(/ 1.0 (sin B))
3.0ms	(/ 1 (tan B))
0.0ms	(fma (- (* x 1.0)) (/ 1 (tan B)) (/ 1.0 (sin B)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ 1.0 (sin B))
31.0ms	(/ 1 (tan B))
103.0ms	(fma (- (* x 1.0)) (/ 1 (tan B)) (/ 1.0 (sin B)))

simplify1.7s

Counts

82 → 82

Iterations

Useful iterations: 4 (786.0ms)

Iter	Nodes	Cost
0	139	761
1	255	695
2	495	625
3	1144	615
4	3461	606
done	5000	606

prune214.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite29.0ms

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))
13.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
8.0ms	(* x (/ 1.0 (sin B)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (sin B))
101.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
59.0ms	(* x (/ 1.0 (sin B)))

simplify2.7s

Counts

127 → 127

Iterations

Useful iterations: 3 (1.4s)

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

prune321.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

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

sample2.4s

Algorithm

intervals

Results

1.0s	1700×	body	1280	valid
530.0ms	1461×	body	640	valid
408.0ms	4889×	body	80	valid
175.0ms	725×	body	320	valid
64.0ms	368×	body	160	valid