Details

sample341.0ms

Algorithm

intervals

Results

86.0ms	146×	body	80	valid
58.0ms	43×	body	640	valid
53.0ms	59×	body	1280	valid
43.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

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))
0.1b	(/ 1.0 (sin B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite67.0ms

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:

18.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
7.0ms	(/ 1.0 (tan B))
7.0ms	(/ 1.0 (sin B))
24.0ms	(* x (/ 1.0 (tan B)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
48.0ms	(/ 1.0 (tan B))
22.0ms	(/ 1.0 (sin B))
139.0ms	(* x (/ 1.0 (tan B)))

simplify1.2s

Counts

115 → 115

Iterations

Useful iterations: done (1.2s)

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

prune506.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))

rewrite117.0ms

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:

87.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
13.0ms	(/ 1.0 (sin B))
14.0ms	(/ (* x 1.0) (tan B))

series433.0ms

Counts

3 → 9

Calls

3 calls:

206.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
38.0ms	(/ 1.0 (sin B))
189.0ms	(/ (* x 1.0) (tan B))

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: done (1.1s)

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

prune302.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

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:

43.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
7.0ms	(/ 1 (sin B))
15.0ms	(* x (cos B))
15.0ms	(/ (* x (cos B)) (sin B))

series422.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
32.0ms	(/ 1 (sin B))
68.0ms	(* x (cos B))
141.0ms	(/ (* x (cos B)) (sin B))

simplify1.3s

Counts

104 → 104

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	145	1077
1	327	981
2	1785	911
done	5000	905

prune341.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

2 → 48

Calls

2 calls:

9.0ms	(* x (cos B))
34.0ms	(/ (- 1 (* x (cos B))) (sin B))

series169.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* x (cos B))
121.0ms	(/ (- 1 (* x (cos B))) (sin B))

simplify671.0ms

Counts

54 → 54

Iterations

Useful iterations: done (669.0ms)

Iter	Nodes	Cost
0	94	632
1	209	607
2	967	559
done	5001	558

prune230.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes116.0ms

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: 0 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	14	11
done	14	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.3s	1742×	body	1280	valid
1.6s	4957×	body	80	valid
1.5s	1462×	body	640	valid
412.0ms	647×	body	320	valid
125.0ms	365×	body	160	valid