Details

sample398.0ms

Algorithm

intervals

Results

34.0ms	152×	body	80	valid
34.0ms	59×	body	1280	valid
14.0ms	41×	body	640	valid
6.0ms	24×	body	320	valid
2.0ms	14×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6
done	53	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

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:

22.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (tan B))
6.0ms	(/ 1.0 (sin B))
20.0ms	(* x (/ 1.0 (tan B)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
40.0ms	(/ 1.0 (tan B))
21.0ms	(/ 1.0 (sin B))
131.0ms	(* x (/ 1.0 (tan B)))

simplify50.0ms

Counts

115 → 115

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	419	664
1	1645	609
2	5001	604
done	5001	604

prune309.0ms

Pruning

10 alts after pruning (10 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)))
0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ 1.0 (sin B))

rewrite67.0ms

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:

48.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
10.0ms	(/ (* x 1.0) (tan B))
7.0ms	(/ 1.0 (sin B))

series261.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
117.0ms	(/ (* x 1.0) (tan B))
20.0ms	(/ 1.0 (sin B))

simplify36.0ms

Counts

74 → 74

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	336	465
1	1303	419
2	5001	414
done	5001	414

prune192.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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	(/ (* x (cos B)) (sin B))
0.2b	(/ 1 (sin B))

rewrite58.0ms

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:

30.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
8.0ms	(* x (cos B))
12.0ms	(/ (* x (cos B)) (sin B))
6.0ms	(/ 1 (sin B))

series254.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
38.0ms	(* x (cos B))
101.0ms	(/ (* x (cos B)) (sin B))
15.0ms	(/ 1 (sin B))

simplify44.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	309	612
1	1342	540
2	5002	535
done	5002	535

prune210.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)))

rewrite124.0ms

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:

88.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
12.0ms	(/ (tan B) (* x 1.0))
5.0ms	(/ 1.0 (sin B))
15.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
55.0ms	(/ (tan B) (* x 1.0))
20.0ms	(/ 1.0 (sin B))
93.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify55.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	531	922
1	2284	808
2	5002	756
done	5002	756

prune269.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7
done	13	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

945.0ms	1701×	body	1280	valid
524.0ms	1454×	body	640	valid
398.0ms	4906×	body	80	valid
163.0ms	715×	body	320	valid
56.0ms	338×	body	160	valid