Details

sample77.0ms

Algorithm

intervals

Results

29.0ms	51×	body	1280	valid
17.0ms	51×	body	640	valid
12.0ms	157×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

localize11.0ms

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

rewrite51.0ms

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:

19.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ 1.0 (tan B))
18.0ms	(* x (/ 1.0 (tan B)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
36.0ms	(/ 1.0 (tan B))
117.0ms	(* x (/ 1.0 (tan B)))

simplify1.6s

Counts

115 → 115

Iterations

Useful iterations: 3 (740.0ms)

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

prune306.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))
0.1b	(/ (* x 1.0) (tan B))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

51.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series261.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
20.0ms	(/ 1.0 (sin B))
118.0ms	(/ (* x 1.0) (tan B))

simplify1.7s

Counts

74 → 74

Iterations

Useful iterations: 3 (810.0ms)

Iter	Nodes	Cost
0	144	837
1	334	797
2	988	711
3	3734	706
done	5000	706

prune179.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (sin B))
0.2b	(* (/ (* x 1.0) (sin B)) (cos B))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

18.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
10.0ms	(/ (* x 1.0) (sin B))
27.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series297.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
60.0ms	(/ (* x 1.0) (sin B))
109.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.0s

Counts

102 → 102

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	165	1259
1	417	1211
2	1482	1044
done	5000	1037

prune239.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
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` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

14.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))

series409.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
97.0ms	(cbrt (sin B))
95.0ms	(cbrt (sin B))
97.0ms	(cbrt (sin B))

simplify1.9s

Counts

85 → 85

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	75	710
1	156	628
2	405	534
3	1260	512
done	5001	507

prune370.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	22	15
3	28	15
done	28	15

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1726×	body	1280	valid
502.0ms	1395×	body	640	valid
393.0ms	4997×	body	80	valid
180.0ms	715×	body	320	valid
58.0ms	354×	body	160	valid