Details

sample409.0ms

Algorithm

intervals

Results

52.0ms	56×	body	1280	valid
16.0ms	180×	body	80	valid
13.0ms	37×	body	640	valid
6.0ms	24×	body	320	valid
1.0ms	7×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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

rewrite50.0ms

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:

15.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
6.0ms	(/ 1.0 (tan B))
5.0ms	(/ 1.0 (sin B))
19.0ms	(* x (/ 1.0 (tan B)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
37.0ms	(/ 1.0 (tan B))
20.0ms	(/ 1.0 (sin B))
134.0ms	(* x (/ 1.0 (tan B)))

simplify1.7s

Counts

129 → 129

Iterations

Useful iterations: 3 (842.0ms)

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

prune362.0ms

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

rewrite74.0ms

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:

53.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
10.0ms	(/ (* x 1.0) (tan B))
8.0ms	(/ 1.0 (sin B))

series260.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
116.0ms	(/ (* x 1.0) (tan B))
22.0ms	(/ 1.0 (sin B))

simplify1.8s

Counts

100 → 100

Iterations

Useful iterations: 3 (868.0ms)

Iter	Nodes	Cost
0	150	887
1	348	843
2	1034	755
3	3935	747
done	5001	747

prune275.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

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:

0.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))
10.0ms	(/ (* x 1.0) (sin B))
5.0ms	(/ 1.0 (sin B))

series186.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(fma (- (/ (* x 1.0) (sin B))) (cos B) (/ 1.0 (sin B)))
57.0ms	(/ (* x 1.0) (sin B))
23.0ms	(/ 1.0 (sin B))

simplify1.9s

Counts

71 → 71

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	120	737
1	259	713
2	750	629
3	2814	629
done	5000	629

prune207.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)))

rewrite136.0ms

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:

97.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
11.0ms	(/ (tan B) (* x 1.0))
5.0ms	(/ 1.0 (sin B))
14.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
53.0ms	(/ (tan B) (* x 1.0))
22.0ms	(/ 1.0 (sin B))
88.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify1.2s

Counts

199 → 199

Iterations

Useful iterations: done (1.2s)

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

prune473.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	20	14
done	20	14

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	1742×	body	1280	valid
508.0ms	1409×	body	640	valid
396.0ms	4896×	body	80	valid
188.0ms	744×	body	320	valid
58.0ms	340×	body	160	valid