Details

sample400.0ms

Algorithm

intervals

Results

57.0ms	62×	body	1280	valid
15.0ms	42×	body	640	valid
13.0ms	169×	body	80	valid
5.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6
done	62	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite57.0ms

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:

22.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
20.0ms	(* x (/ 1.0 (tan B)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
123.0ms	(* x (/ 1.0 (tan B)))

simplify49.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	696
1	1724	639
2	5002	635
done	5002	635

prune338.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite75.0ms

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:

55.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
12.0ms	(/ (* x 1.0) (tan B))

series245.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
110.0ms	(/ (* x 1.0) (tan B))

simplify36.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	350	492
1	1353	445
2	5002	440
done	5002	440

prune267.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

20.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
9.0ms	(/ (cos B) (sin B))
24.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (- (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
19.0ms	(/ (cos B) (sin B))
107.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

simplify49.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	778
1	1654	689
2	5001	684
done	5001	684

prune305.0ms

Pruning

7 alts after pruning (7 fresh and 0 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)))

rewrite62.0ms

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:

5.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (sin B))
33.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
15.0ms	(* x (/ 1.0 (sin B)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (sin B))
105.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
60.0ms	(* x (/ 1.0 (sin B)))

simplify46.0ms

Counts

127 → 127

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	325	672
1	1587	587
2	5001	587
done	5001	587

prune291.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	25	9
2	27	9
3	27	9
done	27	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1746×	body	1280	valid
488.0ms	1395×	body	640	valid
396.0ms	4973×	body	80	valid
190.0ms	743×	body	320	valid
59.0ms	348×	body	160	valid