Details

sample428.0ms

Algorithm

intervals

Results

130.0ms	51×	body	640	valid
85.0ms	69×	body	1280	valid
63.0ms	135×	body	80	valid
12.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* (/ 1.0 (tan B)) x)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

56.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
9.0ms	(/ 1.0 (sin B))
9.0ms	(/ 1.0 (tan B))
34.0ms	(* (/ 1.0 (tan B)) x)

series450.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(- (/ 1.0 (sin B)) (* (/ 1.0 (tan B)) x))
30.0ms	(/ 1.0 (sin B))
51.0ms	(/ 1.0 (tan B))
178.0ms	(* (/ 1.0 (tan B)) x)

simplify1.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1607
1	406
0	176

prune718.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
3×	`pow1` `div-inv`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `flip3--` `diff-log` `tan-quot` `associate-*r/` `associate-/r/` `frac-sub` `flip--` `distribute-lft-out--`

Counts

3 → 69

Calls

3 calls:

43.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ x (tan B))))
9.0ms	(/ 1.0 (sin B))
9.0ms	(/ x (tan B))

series339.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ x (tan B))))
26.0ms	(/ 1.0 (sin B))
147.0ms	(/ x (tan B))

simplify861.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
2	1005
1	317
0	149

prune463.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

38.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
8.0ms	(/ 1.0 (sin B))
13.0ms	(* x (cos B))
19.0ms	(/ (* x (cos B)) (sin B))

series411.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
29.0ms	(/ 1.0 (sin B))
50.0ms	(* x (cos B))
131.0ms	(/ (* x (cos B)) (sin B))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1464
1	355
0	150

prune554.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

40.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
8.0ms	(/ 1.0 (sin B))
8.0ms	(/ x (sin B))
49.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

series426.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(- (/ 1.0 (sin B)) (* (* 1.0 (/ x (sin B))) (cos B)))
32.0ms	(/ 1.0 (sin B))
76.0ms	(/ x (sin B))
151.0ms	(* (* 1.0 (/ x (sin B))) (cos B))

simplify1.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1898
1	403
0	169

prune542.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes141.0ms

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	12
1	12
0	10

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.1s	1661×	body	1280	valid
2.0s	1489×	body	640	valid
1.0s	4896×	body	80	valid
329.0ms	720×	body	320	valid
172.0ms	350×	body	160	valid