Details

sample183.0ms

Algorithm

intervals

Results

61.0ms	40×	body	640	valid
60.0ms	58×	body	1280	valid
26.0ms	166×	body	80	valid
8.0ms	16×	body	320	valid
6.0ms	17×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	59	11
6	61	11
done	61	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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)))

rewrite51.0ms

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:

17.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
19.0ms	(* x (/ 1.0 (tan B)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
60.0ms	(/ 1.0 (tan B))
173.0ms	(* x (/ 1.0 (tan B)))

simplify2.8s

Counts

129 → 129

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	188	1244
1	433	1180
2	1188	1075
3	3683	1067
done	5001	1067

prune521.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.1b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
107×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
98×	`add-cube-cbrt`
91×	`prod-diff`
28×	`div-inv`
15×	`add-exp-log`
13×	`fma-neg` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `distribute-rgt-out--` `associate-r` `associate-l` `difference-of-squares`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 204

Calls

4 calls:

54.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(* x (cos B))
12.0ms	(/ 1 (sin B))
17.0ms	(/ (* x (cos B)) (sin B))

series358.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
62.0ms	(* x (cos B))
15.0ms	(/ 1 (sin B))
127.0ms	(/ (* x (cos B)) (sin B))

simplify1.7s

Counts

216 → 216

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	264	6388
1	574	4918
2	1409	3868
done	5001	3101

prune478.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan B)) (cbrt (tan B)))
0.5b	(cbrt (tan B))
0.5b	(cbrt (tan B))
0.5b	(cbrt (tan B))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
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` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

20.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))
8.0ms	(cbrt (tan B))

series731.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
185.0ms	(cbrt (tan B))
166.0ms	(cbrt (tan B))
153.0ms	(cbrt (tan B))

simplify1.6s

Counts

99 → 99

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	90	824
1	176	740
2	391	695
3	819	651
4	1909	646
done	5000	614

prune484.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(cbrt (/ 1.0 (sin B)))
0.5b	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `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 → 152

Calls

4 calls:

3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
65.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series903.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt (/ 1.0 (sin B)))
204.0ms	(cbrt (/ 1.0 (sin B)))
197.0ms	(cbrt (/ 1.0 (sin B)))
283.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify2.0s

Counts

164 → 164

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	174	2305
1	310	2134
2	849	2047
3	2160	1938
done	5000	1929

prune980.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
done	15	14

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.6s	1730×	body	1280	valid
1.6s	1449×	body	640	valid
1.2s	4913×	body	80	valid
331.0ms	705×	body	320	valid
213.0ms	339×	body	160	valid