Details

sample450.0ms

Algorithm

intervals

Results

85.0ms	20×	body	320	valid
83.0ms	188×	body	80	valid
55.0ms	38×	body	1280	valid
44.0ms	43×	body	640	valid
41.0ms	12×	body	160	valid

simplify132.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize140.0ms

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)))

rewrite125.0ms

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:

35.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
14.0ms	(/ 1.0 (sin B))
14.0ms	(/ 1.0 (tan B))
50.0ms	(* x (/ 1.0 (tan B)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
32.0ms	(/ 1.0 (sin B))
40.0ms	(/ 1.0 (tan B))
178.0ms	(* x (/ 1.0 (tan B)))

simplify2.6s

Counts

115 → 115

Iterations

Useful iterations: 3 (1.2s)

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

prune427.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite121.0ms

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:

94.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
11.0ms	(/ (* x 1.0) (tan B))
13.0ms	(/ 1.0 (sin B))

series419.0ms

Counts

3 → 9

Calls

3 calls:

218.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
168.0ms	(/ (* x 1.0) (tan B))
32.0ms	(/ 1.0 (sin B))

simplify2.9s

Counts

74 → 74

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	144	837
1	334	797
2	992	711
3	3763	706
done	5001	706

prune358.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

36.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
48.0ms	(* (* 1.0 (/ x (sin B))) (cos B))
11.0ms	(/ x (sin B))

series419.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ (- (* (* 1.0 (/ x (sin B))) (cos B))) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (sin B))
156.0ms	(* (* 1.0 (/ x (sin B))) (cos B))
68.0ms	(/ x (sin B))

simplify2.1s

Counts

102 → 102

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	173	1214
1	406	1164
2	1356	1019
done	5001	1012

prune428.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos B)) (cbrt (cos B)))
0.3b	(cbrt (cos B))
0.3b	(cbrt (cos B))
0.3b	(cbrt (cos 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`
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:

22.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
2.0ms	(cbrt (cos B))
3.0ms	(cbrt (cos B))
3.0ms	(cbrt (cos B))

series696.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (cbrt (cos B)) (cbrt (cos B)))
167.0ms	(cbrt (cos B))
146.0ms	(cbrt (cos B))
140.0ms	(cbrt (cos B))

simplify6.1s

Counts

85 → 85

Iterations

Useful iterations: 4 (3.5s)

Iter	Nodes	Cost
0	64	686
1	122	615
2	336	521
3	1141	499
4	4988	492
done	5001	492

prune351.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	26	15
3	28	15
done	28	15

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.2s	1431×	body	640	valid
2.0s	1697×	body	1280	valid
1.0s	709×	body	320	valid
1.0s	4914×	body	80	valid
163.0ms	342×	body	160	valid