Details

sample142.0ms

Algorithm

intervals

Results

59.0ms	58×	body	1280	valid
25.0ms	40×	body	640	valid
24.0ms	166×	body	80	valid
7.0ms	16×	body	320	valid
6.0ms	17×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
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` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

16.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
16.0ms	(/ 1.0 (sin B))
10.0ms	(/ 1.0 (tan B))
31.0ms	(* x (/ 1.0 (tan B)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
21.0ms	(/ 1.0 (sin B))
57.0ms	(/ 1.0 (tan B))
148.0ms	(* x (/ 1.0 (tan B)))

simplify2.4s

Counts

115 → 115

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	180	1184
1	414	1125
2	1121	1022
3	3390	1017
done	5000	1017

prune478.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))

rewrite67.0ms

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:

33.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms	(* x (cos B))
7.0ms	(/ 1 (sin B))
13.0ms	(/ (* x (cos B)) (sin B))

series340.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
59.0ms	(* x (cos B))
19.0ms	(/ 1 (sin B))
130.0ms	(/ (* x (cos B)) (sin B))

simplify3.7s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.8s)

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

prune350.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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))

rewrite32.0ms

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:

22.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))

series759.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
179.0ms	(cbrt (tan B))
140.0ms	(cbrt (tan B))
195.0ms	(cbrt (tan B))

simplify1.9s

Counts

91 → 91

Iterations

Useful iterations: done (1.9s)

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

prune538.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

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))))

rewrite59.0ms

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:

6.0ms	(cbrt (/ 1.0 (sin B)))
5.0ms	(cbrt (/ 1.0 (sin B)))
3.0ms	(cbrt (/ 1.0 (sin B)))
31.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

series939.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(cbrt (/ 1.0 (sin B)))
248.0ms	(cbrt (/ 1.0 (sin B)))
203.0ms	(cbrt (/ 1.0 (sin B)))
293.0ms	(* (cbrt (/ 1.0 (sin B))) (cbrt (/ 1.0 (sin B))))

simplify1.8s

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

prune856.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	23	28
2	31	28
3	35	28
4	37	28
done	37	28

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.1s	1730×	body	1280	valid
1.4s	1449×	body	640	valid
1.3s	4913×	body	80	valid
451.0ms	705×	body	320	valid
164.0ms	339×	body	160	valid