Details

sample290.0ms

Algorithm

intervals

Results

89.0ms	166×	body	80	valid
69.0ms	58×	body	1280	valid
32.0ms	40×	body	640	valid
8.0ms	16×	body	320	valid
6.0ms	17×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	52	11
done	52	11

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 101

Calls

4 calls:

34.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
6.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
38.0ms	(* x (/ 1.0 (tan B)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
22.0ms	(/ 1.0 (sin B))
50.0ms	(/ 1.0 (tan B))
143.0ms	(* x (/ 1.0 (tan B)))

simplify2.6s

Counts

113 → 113

Iterations

Useful iterations: 2 (276.0ms)

Iter	Nodes	Cost
0	174	1141
1	383	1074
2	964	996
3	2656	996
done	5000	996

prune440.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`add-exp-log` `times-frac`
13×	`add-cbrt-cube`
7×	`pow1` `div-inv`
6×	`associate-/r*` `add-log-exp`
4×	`div-exp` `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 → 92

Calls

4 calls:

58.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(* x (cos B))
7.0ms	(/ 1 (sin B))
15.0ms	(/ (* x (cos B)) (sin B))

series363.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
56.0ms	(* x (cos B))
17.0ms	(/ 1 (sin B))
133.0ms	(/ (* x (cos B)) (sin B))

simplify3.9s

Counts

104 → 104

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	145	1077
1	307	981
2	857	905
3	4209	887
done	5000	887

prune382.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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))

rewrite54.0ms

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×	`add-cbrt-cube` `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 → 79

Calls

4 calls:

38.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
3.0ms	(cbrt (tan B))
4.0ms	(cbrt (tan B))
4.0ms	(cbrt (tan B))

series763.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
229.0ms	(cbrt (tan B))
154.0ms	(cbrt (tan B))
177.0ms	(cbrt (tan B))

simplify1.6s

Counts

91 → 91

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	86	784
1	170	704
2	374	660
3	750	621
4	1814	616
done	5000	586

prune391.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

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))))

rewrite75.0ms

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×	`add-cbrt-cube` `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 → 144

Calls

4 calls:

3.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
4.0ms	(cbrt (/ 1.0 (sin B)))
58.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series923.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (/ 1.0 (sin B)))
183.0ms	(cbrt (/ 1.0 (sin B)))
263.0ms	(cbrt (/ 1.0 (sin B)))
268.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify1.9s

Counts

156 → 156

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	170	2245
1	302	2082
2	826	1991
3	2021	1888
done	5001	1883

prune677.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.7s	1730×	body	1280	valid
1.8s	1449×	body	640	valid
1.5s	4913×	body	80	valid
397.0ms	705×	body	320	valid
161.0ms	339×	body	160	valid