Details

sample326.0ms

Algorithm

intervals

Results

32.0ms	55×	body	1280	valid
16.0ms	45×	body	640	valid
14.0ms	169×	body	80	valid
3.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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:

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)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
38.0ms	(/ 1.0 (tan B))
122.0ms	(* x (/ 1.0 (tan B)))

simplify735.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	188	1244
1	438	1180
2	1373	1075
done	5000	1075

prune356.0ms

Pruning

9 alts after pruning (9 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))
0.1b	(/ (* x 1.0) (tan B))

rewrite39.0ms

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:

30.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms	(/ 1.0 (sin B))
4.0ms	(/ (* x 1.0) (tan B))

series239.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
107.0ms	(/ (* x 1.0) (tan B))

simplify1.9s

Counts

100 → 100

Iterations

Useful iterations: 3 (734.0ms)

Iter	Nodes	Cost
0	150	887
1	350	843
2	1067	755
3	4886	749
done	5000	749

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 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))
0.2b	(* x (/ 1.0 (sin B)))

rewrite28.0ms

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)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (sin B))
98.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
56.0ms	(* x (/ 1.0 (sin B)))

simplify660.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	140	1194
1	325	1146
2	1185	1002
done	5000	1002

prune332.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series712.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt x) (cbrt x))
169.0ms	(cbrt x)
167.0ms	(cbrt x)
176.0ms	(cbrt x)

simplify1.4s

Counts

93 → 93

Iterations

Useful iterations: 3 (327.0ms)

Iter	Nodes	Cost
0	65	554
1	119	443
2	383	423
3	1868	405
done	5000	405

prune265.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	20	19
2	30	19
3	32	19
done	32	19

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	1744×	body	1280	valid
508.0ms	1436×	body	640	valid
385.0ms	4907×	body	80	valid
166.0ms	717×	body	320	valid
57.0ms	350×	body	160	valid