Details

sample749.0ms

Algorithm

intervals

Results

37.0ms	50×	body	1280	valid
20.0ms	168×	body	80	valid
19.0ms	42×	body	640	valid
7.0ms	17×	body	320	valid
3.0ms	12×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	52
6	52
5	50
4	44
3	37
2	31
1	18
0	10

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

103.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
17.0ms	(/ 1.0 (sin B))
117.0ms	(/ (* x 1.0) (tan B))

series434.0ms

Counts

3 → 9

Calls

3 calls:

154.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
38.0ms	(/ 1.0 (sin B))
242.0ms	(/ (* x 1.0) (tan B))

simplify1.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1078
1	338
0	144

prune540.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))

rewrite75.0ms

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:

40.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
10.0ms	(/ 1.0 (sin B))
9.0ms	(* x (cos B))
12.0ms	(/ (* x (cos B)) (sin B))

series332.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
21.0ms	(/ 1.0 (sin B))
46.0ms	(* x (cos B))
124.0ms	(/ (* x (cos B)) (sin B))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1138
1	353
0	150

prune561.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
2×	`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 → 48

Calls

2 calls:

14.0ms	(* x (cos B))
26.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

series188.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(* x (cos B))
127.0ms	(/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B))

simplify2.1s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	2755
2	703
1	236
0	103

prune406.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

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

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

48.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
9.0ms	(/ 1.0 (sin B))
23.0ms	(/ (* x 1.0) (sin B))
29.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series469.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
25.0ms	(/ 1.0 (sin B))
77.0ms	(/ (* x 1.0) (sin B))
172.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.7s

Counts

101 → 101

Iterations

Iter	Nodes
done	5003
2	1594
1	418
0	161

prune562.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes196.0ms

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	11
1	11
0	9

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.6s	1745×	body	1280	valid
1.6s	1413×	body	640	valid
1.1s	4926×	body	80	valid
351.0ms	739×	body	320	valid
104.0ms	332×	body	160	valid