Details

sample112.0ms

Algorithm

intervals

Results

39.0ms	52×	body	1280	valid
28.0ms	54×	body	640	valid
17.0ms	148×	body	80	valid
10.0ms	23×	body	320	valid
3.0ms	13×	body	160	valid

simplify92.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	56
6	56
5	54
4	48
3	41
2	33
1	18
0	10

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

3 → 188

Calls

3 calls:

38.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
4.0ms	(/ 1.0 (sin B))
12.0ms	(/ (* x 1.0) (tan B))

series357.0ms

Counts

3 → 9

Calls

3 calls:

174.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
28.0ms	(/ 1.0 (sin B))
155.0ms	(/ (* x 1.0) (tan B))

simplify1.7s

Counts

197 → 197

Iterations

Iter	Nodes
done	5000
2	1836
1	680
0	285

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

687×	`times-frac`
418×	`add-sqr-sqrt`
410×	`*-un-lft-identity`
401×	`add-cube-cbrt`
338×	`prod-diff`
87×	`div-inv`
32×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`div-exp`
14×	`associate-/r/`
13×	`fma-neg`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `distribute-lft-out--`
2×	`cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `frac-sub` `pow-flip` `flip--` `inv-pow` `associate-/l/`

Counts

4 → 486

Calls

4 calls:

61.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
4.0ms	(/ 1.0 (sin B))
7.0ms	(/ (tan B) (* x 1.0))
14.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
29.0ms	(/ 1.0 (sin B))
71.0ms	(/ (tan B) (* x 1.0))
112.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify2.1s

Counts

498 → 498

Iterations

Iter	Nodes
done	5004
2	3390
1	1571
0	664

prune3.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac`
102×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
97×	`add-cube-cbrt`
91×	`prod-diff`
25×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
13×	`fma-neg`
9×	`pow1`
6×	`associate-/r*` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `associate-/l*`
3×	`associate-l` `pow-prod-down`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `associate-r` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 198

Calls

4 calls:

31.0ms	(- (/ 1.0 (sin B)) (/ (* (cos B) (* 1.0 x)) (sin B)))
13.0ms	(* (cos B) (* 1.0 x))
6.0ms	(/ 1.0 (sin B))
24.0ms	(/ (* (cos B) (* 1.0 x)) (sin B))

series330.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (/ 1.0 (sin B)) (/ (* (cos B) (* 1.0 x)) (sin B)))
67.0ms	(* (cos B) (* 1.0 x))
20.0ms	(/ 1.0 (sin B))
102.0ms	(/ (* (cos B) (* 1.0 x)) (sin B))

simplify1.4s

Counts

210 → 210

Iterations

Iter	Nodes
done	5029
2	2254
1	716
0	289

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (cos B) (/ (sin B) (* 1.0 x))))
0.1b	(/ 1.0 (sin B))
0.1b	(/ (sin B) (* 1.0 x))
0.3b	(/ (cos B) (/ (sin B) (* 1.0 x)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

684×	`times-frac`
413×	`add-sqr-sqrt`
407×	`*-un-lft-identity`
401×	`add-cube-cbrt`
338×	`prod-diff`
86×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r/`
13×	`fma-neg`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `difference-of-squares`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 474

Calls

4 calls:

77.0ms	(- (/ 1.0 (sin B)) (/ (cos B) (/ (sin B) (* 1.0 x))))
4.0ms	(/ 1.0 (sin B))
12.0ms	(/ (sin B) (* 1.0 x))
25.0ms	(/ (cos B) (/ (sin B) (* 1.0 x)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(- (/ 1.0 (sin B)) (/ (cos B) (/ (sin B) (* 1.0 x))))
26.0ms	(/ 1.0 (sin B))
49.0ms	(/ (sin B) (* 1.0 x))
109.0ms	(/ (cos B) (/ (sin B) (* 1.0 x)))

simplify3.2s

Counts

486 → 486

Iterations

Iter	Nodes
done	5000
2	4501
1	1602
0	666

prune4.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.7s	1710×	body	1280	valid
1.2s	1422×	body	640	valid
912.0ms	4905×	body	80	valid
557.0ms	379×	body	160	valid
511.0ms	700×	body	320	valid