Details

sample458.0ms

Algorithm

intervals

Results

159.0ms	60×	body	1280	valid
67.0ms	144×	body	80	valid
37.0ms	45×	body	640	valid
16.0ms	25×	body	320	valid
5.0ms	7×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	53	11
done	53	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

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)))
7.0ms	(/ 1.0 (tan B))
6.0ms	(/ 1.0 (sin B))
23.0ms	(* x (/ 1.0 (tan B)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
53.0ms	(/ 1.0 (tan B))
24.0ms	(/ 1.0 (sin B))
147.0ms	(* x (/ 1.0 (tan B)))

simplify1.0s

Counts

115 → 115

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	180	1184
1	443	1129
2	1635	1030
done	5001	1023

prune559.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite107.0ms

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:

81.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
12.0ms	(/ 1.0 (sin B))
12.0ms	(/ (* x 1.0) (tan B))

series408.0ms

Counts

3 → 9

Calls

3 calls:

204.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
41.0ms	(/ 1.0 (sin B))
163.0ms	(/ (* x 1.0) (tan B))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	144	837
1	357	797
2	1524	715
done	5001	714

prune343.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
0.2b	(/ (tan B) (* x 1.0))
0.2b	(/ 1.0 (sin B))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `distribute-lft-out`
3×	`rec-exp` `distribute-rgt-neg-in` `frac-2neg` `1-exp` `clear-num`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `pow-flip` `flip3-+` `neg-log` `frac-add` `associate-/r/` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 123

Calls

4 calls:

144.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
10.0ms	(/ (tan B) (* x 1.0))
6.0ms	(/ 1.0 (sin B))
28.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
81.0ms	(/ (tan B) (* x 1.0))
24.0ms	(/ 1.0 (sin B))
145.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.6s

Counts

135 → 135

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	227	1699
1	572	1515
2	2442	1323
done	5002	1317

prune546.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ (/ 1 (tan B)) (/ 1 (* x 1.0)))) (/ 1.0 (sin B)))
0.1b	(/ 1 (tan B))
0.2b	(/ 1.0 (sin B))
0.3b	(/ (/ 1 (tan B)) (/ 1 (* x 1.0)))

rewrite568.0ms

Algorithm

rewrite-expression-head

Rules

241×	`times-frac`
122×	`*-un-lft-identity`
106×	`add-sqr-sqrt` `add-cube-cbrt`
93×	`add-exp-log`
61×	`div-exp`
30×	`div-inv`
29×	`add-cbrt-cube`
20×	`associate-/l*`
16×	`rec-exp` `1-exp`
15×	`cbrt-undiv`
13×	`associate-/r*`
12×	`prod-exp`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-log-exp`
6×	`distribute-lft-out`
5×	`pow1` `distribute-rgt-neg-in`
3×	`frac-2neg` `clear-num`
2×	`sum-log` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `pow-flip` `flip3-+` `neg-log` `frac-add` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 244

Calls

4 calls:

492.0ms	(+ (- (/ (/ 1 (tan B)) (/ 1 (* x 1.0)))) (/ 1.0 (sin B)))
8.0ms	(/ 1 (tan B))
6.0ms	(/ 1.0 (sin B))
49.0ms	(/ (/ 1 (tan B)) (/ 1 (* x 1.0)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(+ (- (/ (/ 1 (tan B)) (/ 1 (* x 1.0)))) (/ 1.0 (sin B)))
63.0ms	(/ 1 (tan B))
39.0ms	(/ 1.0 (sin B))
128.0ms	(/ (/ 1 (tan B)) (/ 1 (* x 1.0)))

simplify756.0ms

Counts

256 → 256

Iterations

Useful iterations: done (745.0ms)

Iter	Nodes	Cost
0	391	4208
1	1190	3584
done	5000	3111

prune612.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes100.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 2 (3.0ms)

Iter	Nodes	Cost
0	13	16
1	19	16
2	22	15
done	22	15

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.4s	1696×	body	1280	valid
1.6s	1371×	body	640	valid
1.6s	4973×	body	80	valid
344.0ms	715×	body	320	valid
143.0ms	388×	body	160	valid