Details

sample92.0ms

Algorithm

intervals

Results

37.0ms	53×	body	1280	valid
17.0ms	39×	body	640	valid
15.0ms	157×	body	80	valid
7.0ms	24×	body	320	valid
2.0ms	10×	body	160	valid

simplify89.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	59	11
6	61	11
done	61	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

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)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `fma-def` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `distribute-lft-neg-in` `associate-+l-` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 117

Calls

4 calls:

29.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (tan B))
10.0ms	(/ 1.0 (sin B))
32.0ms	(* x (/ 1.0 (tan B)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
51.0ms	(/ 1.0 (tan B))
29.0ms	(/ 1.0 (sin B))
178.0ms	(* x (/ 1.0 (tan B)))

simplify2.4s

Counts

129 → 129

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	188	1244
1	433	1180
2	1188	1075
3	3696	1067
done	5001	1067

prune381.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`fma-def`
18×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-rgt-neg-in`
8×	`distribute-lft-neg-in`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`tan-quot` `pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 91

Calls

3 calls:

59.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series332.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
27.0ms	(/ 1.0 (sin B))
158.0ms	(/ (* x 1.0) (tan B))

simplify2.2s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	150	887
1	348	843
2	1039	755
3	3938	747
done	5000	747

prune381.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ (* x 1.0) (sin B))
0.1b	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`prod-exp` `cbrt-unprod` `fma-udef`

Counts

3 → 62

Calls

3 calls:

6.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (sin B))
0.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ 1.0 (sin B))
88.0ms	(/ (* x 1.0) (sin B))
152.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))

simplify2.6s

Counts

71 → 71

Iterations

Useful iterations: 2 (162.0ms)

Iter	Nodes	Cost
0	120	737
1	259	713
2	749	629
3	2777	629
done	5000	629

prune279.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

107×	`times-frac`
68×	`*-un-lft-identity`
59×	`add-sqr-sqrt` `add-cube-cbrt`
56×	`fma-def`
32×	`add-exp-log`
29×	`distribute-rgt-neg-in`
26×	`distribute-lft-neg-in`
20×	`add-cbrt-cube`
16×	`div-inv`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/r/`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `pow-flip` `flip3-+` `neg-log` `frac-add` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 187

Calls

4 calls:

170.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
10.0ms	(/ (tan B) (* x 1.0))
6.0ms	(/ 1.0 (sin B))
23.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
62.0ms	(/ (tan B) (* x 1.0))
31.0ms	(/ 1.0 (sin B))
123.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify2.1s

Counts

199 → 199

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	235	1771
1	538	1578
2	1427	1329
done	5001	1322

prune1.2s

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

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	19	14
done	19	14

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.8s	1741×	body	1280	valid
1.1s	1384×	body	640	valid
1.0s	713×	body	320	valid
917.0ms	4950×	body	80	valid
120.0ms	351×	body	160	valid