Details

sample254.0ms

Algorithm

intervals

Results

81.0ms	162×	body	80	valid
52.0ms	55×	body	1280	valid
30.0ms	51×	body	640	valid
9.0ms	21×	body	320	valid
4.0ms	15×	body	160	valid

simplify121.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

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

rewrite122.0ms

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:

47.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
13.0ms	(/ 1.0 (tan B))
45.0ms	(* x (/ 1.0 (tan B)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
29.0ms	(/ 1.0 (sin B))
67.0ms	(/ 1.0 (tan B))
192.0ms	(* x (/ 1.0 (tan B)))

simplify1.2s

Counts

129 → 129

Iterations

Useful iterations: done (1.2s)

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

prune600.0ms

Pruning

11 alts after pruning (11 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	(/ 1.0 (sin B))
0.2b	(/ (* x 1.0) (tan B))

rewrite133.0ms

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:

94.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
24.0ms	(/ (* x 1.0) (tan B))

series399.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
184.0ms	(/ (* x 1.0) (tan B))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	150	887
1	369	843
2	1548	761
done	5000	752

prune413.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite115.0ms

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:

7.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (sin B))
65.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
33.0ms	(* x (/ 1.0 (sin B)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1.0 (sin B))
38.0ms	(/ 1.0 (sin B))
167.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
90.0ms	(* x (/ 1.0 (sin B)))

simplify1.5s

Counts

127 → 127

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	140	1194
1	347	1150
2	1633	1022
done	5001	1014

prune556.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
0.6b	(cbrt (/ 1.0 (tan B)))
0.6b	(cbrt (/ 1.0 (tan B)))
0.6b	(cbrt (/ 1.0 (tan B)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

110×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`tan-quot` `cbrt-div` `associate-/r/` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

61.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
4.0ms	(cbrt (/ 1.0 (tan B)))
4.0ms	(cbrt (/ 1.0 (tan B)))
4.0ms	(cbrt (/ 1.0 (tan B)))

series974.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
239.0ms	(cbrt (/ 1.0 (tan B)))
228.0ms	(cbrt (/ 1.0 (tan B)))
229.0ms	(cbrt (/ 1.0 (tan B)))

simplify1.4s

Counts

170 → 170

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	185	2379
1	365	2212
2	1600	2130
done	5000	2069

prune883.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify11.0ms

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

sample6.1s

Algorithm

intervals

Results

2.3s	1707×	body	1280	valid
1.8s	4885×	body	80	valid
1.1s	1450×	body	640	valid
319.0ms	693×	body	320	valid
178.0ms	370×	body	160	valid