Details

sample749.0ms

Algorithm

intervals

Results

575.0ms	50×	body	1280	valid
54.0ms	168×	body	80	valid
20.0ms	42×	body	640	valid
5.0ms	17×	body	320	valid
3.0ms	12×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

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))

rewrite69.0ms

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:

35.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
4.0ms	(/ 1.0 (sin B))
11.0ms	(/ (* x 1.0) (tan B))

series373.0ms

Counts

3 → 9

Calls

3 calls:

184.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
38.0ms	(/ 1.0 (sin B))
151.0ms	(/ (* x 1.0) (tan B))

simplify1.9s

Counts

197 → 197

Iterations

Iter	Nodes
done	5000
2	1836
1	680
0	285

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `fma-neg` `prod-diff` `add-exp-log`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

48.0ms	(- (/ 1.0 (sin B)) (* (/ (* x (cos B)) (sin B)) 1.0))
8.0ms	(/ 1.0 (sin B))
19.0ms	(* x (cos B))
10.0ms	(/ (* x (cos B)) (sin B))

series415.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(- (/ 1.0 (sin B)) (* (/ (* x (cos B)) (sin B)) 1.0))
22.0ms	(/ 1.0 (sin B))
69.0ms	(* x (cos B))
151.0ms	(/ (* x (cos B)) (sin B))

simplify1.5s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1379
1	415
0	173

prune860.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `distribute-rgt-out--` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

2 → 56

Calls

2 calls:

25.0ms	(/ (- 1.0 (* (* x (cos B)) 1.0)) (sin B))
7.0ms	(* x (cos B))

series163.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(/ (- 1.0 (* (* x (cos B)) 1.0)) (sin B))
51.0ms	(* x (cos B))

simplify2.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
3	2772
2	745
1	269
0	115

prune372.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

507×	`times-frac`
276×	`add-sqr-sqrt`
273×	`*-un-lft-identity`
271×	`add-cube-cbrt`
234×	`prod-diff`
50×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/r*`
14×	`associate-/r/`
13×	`fma-neg`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `cbrt-unprod` `difference-of-squares`
1×	`quot-tan` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 372

Calls

4 calls:

48.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (/ (sin B) (cos B))))
5.0ms	(/ 1.0 (sin B))
26.0ms	(/ (* x 1.0) (/ (sin B) (cos B)))
13.0ms	(/ (sin B) (cos B))

series417.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (/ (sin B) (cos B))))
40.0ms	(/ 1.0 (sin B))
179.0ms	(/ (* x 1.0) (/ (sin B) (cos B)))
23.0ms	(/ (sin B) (cos B))

simplify2.6s

Counts

384 → 384

Iterations

Iter	Nodes
done	5000
2	4032
1	1300
0	526

prune3.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.2s	1745×	body	1280	valid
2.0s	4926×	body	80	valid
1.4s	1413×	body	640	valid
364.0ms	739×	body	320	valid
147.0ms	332×	body	160	valid