Details

sample296.0ms

Algorithm

intervals

Results

120.0ms	55×	body	1280	valid
41.0ms	53×	body	640	valid
29.0ms	154×	body	80	valid
13.0ms	21×	body	320	valid
4.0ms	10×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	10	12
1	31	12
2	55	11
done	55	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
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` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

27.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (tan B))
49.0ms	(* x (/ 1.0 (tan B)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
31.0ms	(/ 1.0 (sin B))
77.0ms	(/ 1.0 (tan B))
179.0ms	(* x (/ 1.0 (tan B)))

simplify6.6s

Counts

115 → 115

Iterations

Useful iterations: done (6.6s)

Iter	Nodes	Cost
0	180	1184
1	2302	1119
done	5000	1035

prune497.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

72.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
7.0ms	(/ 1.0 (sin B))
13.0ms	(/ (* x 1.0) (tan B))

series386.0ms

Counts

3 → 9

Calls

3 calls:

206.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
154.0ms	(/ (* x 1.0) (tan B))

simplify5.7s

Counts

74 → 74

Iterations

Useful iterations: done (5.7s)

Iter	Nodes	Cost
0	144	837
1	1230	793
done	5000	716

prune348.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

16.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
13.0ms	(* x (cos B))
11.0ms	(/ 1.0 (sin B))
21.0ms	(/ (* x (cos B)) (sin B))

series437.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
65.0ms	(* x (cos B))
25.0ms	(/ 1.0 (sin B))
152.0ms	(/ (* x (cos B)) (sin B))

simplify6.2s

Counts

94 → 94

Iterations

Useful iterations: done (6.2s)

Iter	Nodes	Cost
0	154	1045
1	2031	985
done	5000	891

prune396.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-log-exp`
7×	`associate-l`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

18.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
9.0ms	(/ 1.0 (sin B))
21.0ms	(/ (* x 1.0) (sin B))
49.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series405.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
26.0ms	(/ 1.0 (sin B))
83.0ms	(/ (* x 1.0) (sin B))
141.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify6.3s

Counts

102 → 102

Iterations

Useful iterations: done (6.3s)

Iter	Nodes	Cost
0	165	1259
1	2787	1207
done	5000	1061

prune403.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	20	15
2	22	15
3	28	15
done	28	15

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.4s	1706×	body	1280	valid
1.4s	4938×	body	80	valid
1.4s	1451×	body	640	valid
501.0ms	726×	body	320	valid
107.0ms	334×	body	160	valid