Details

sample159.0ms

Algorithm

intervals

Results

64.0ms	57×	body	1280	valid
34.0ms	48×	body	640	valid
26.0ms	155×	body	80	valid
10.0ms	20×	body	320	valid
2.0ms	7×	body	160	valid

simplify85.0ms

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	53	11
done	53	11

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`times-frac` `add-cube-cbrt`
14×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`clear-num` `sum-log` `frac-2neg` `prod-exp` `tan-quot` `associate-*r/` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `+-commutative` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `associate-+l-` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

36.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
14.0ms	(* x (/ 1.0 (tan B)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
36.0ms	(/ 1.0 (sin B))
62.0ms	(/ 1.0 (tan B))
164.0ms	(* x (/ 1.0 (tan B)))

simplify869.0ms

Counts

115 → 115

Iterations

Useful iterations: done (865.0ms)

Iter	Nodes	Cost
0	181	1184
1	444	1129
2	1638	1030
done	5000	1023

prune682.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac` `add-exp-log`
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×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

46.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
13.0ms	(* x (cos B))
10.0ms	(/ 1 (sin B))
9.0ms	(/ (* x (cos B)) (sin B))

series343.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
56.0ms	(* x (cos B))
26.0ms	(/ 1 (sin B))
138.0ms	(/ (* x (cos B)) (sin B))

simplify985.0ms

Counts

104 → 104

Iterations

Useful iterations: done (981.0ms)

Iter	Nodes	Cost
0	146	1077
1	328	981
2	1806	911
done	5001	905

prune752.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `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 → 73

Calls

4 calls:

1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
12.0ms	(* (cbrt (sin B)) (cbrt (sin B)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (sin B))
144.0ms	(cbrt (sin B))
166.0ms	(cbrt (sin B))
199.0ms	(* (cbrt (sin B)) (cbrt (sin B)))

simplify1.3s

Counts

85 → 85

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	75	710
1	177	628
2	695	534
done	5000	520

prune467.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
0.4b	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
0.4b	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
0.5b	(* (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))) (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-*r/`
11×	`pow1` `flip3--` `frac-sub` `flip--`
9×	`frac-times` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-*l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

19.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
20.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
21.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
115.0ms	(* (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))) (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))

series950.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
245.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
235.0ms	(cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))
248.0ms	(* (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))) (cbrt (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))

simplify951.0ms

Counts

109 → 109

Iterations

Useful iterations: done (947.0ms)

Iter	Nodes	Cost
0	201	3926
1	504	3710
2	2021	3491
done	5000	3258

prune741.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.9s	1690×	body	1280	valid
1.1s	4996×	body	80	valid
1.0s	1437×	body	640	valid
417.0ms	710×	body	320	valid
214.0ms	377×	body	160	valid