Details

sample188.0ms

Algorithm

intervals

Results

60.0ms	156×	body	80	valid
40.0ms	56×	body	1280	valid
17.0ms	38×	body	640	valid
8.0ms	27×	body	320	valid
4.0ms	17×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize77.0ms

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)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`times-frac` `add-cube-cbrt`
14×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`clear-num` `sum-log` `frac-2neg` `prod-exp` `tan-quot` `associate-*r/` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `+-commutative` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `associate-+l-` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

14.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
5.0ms	(/ 1.0 (tan B))
29.0ms	(* x (/ 1.0 (tan B)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
39.0ms	(/ 1.0 (sin B))
60.0ms	(/ 1.0 (tan B))
186.0ms	(* x (/ 1.0 (tan B)))

simplify1.0s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1638
1	444
0	181

prune715.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))
0.1b	(/ (* x 1.0) (tan B))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

48.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
8.0ms	(/ (* x 1.0) (tan B))

series388.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
37.0ms	(/ 1.0 (sin B))
179.0ms	(/ (* x 1.0) (tan B))

simplify1.0s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1506
1	358
0	145

prune424.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `sum-log` `frac-2neg` `associate-*l/`
1×	`neg-sub0` `+-commutative` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `associate-+l-` `flip-+` `distribute-neg-frac` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

21.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
8.0ms	(/ 1.0 (sin B))
15.0ms	(/ (* x 1.0) (sin B))
26.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series446.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(+ (- (* (/ (* x 1.0) (sin B)) (cos B))) (/ 1.0 (sin B)))
22.0ms	(/ 1.0 (sin B))
85.0ms	(/ (* x 1.0) (sin B))
157.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2326
1	448
0	166

prune638.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
64×	`*-un-lft-identity`
62×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
8×	`add-log-exp`
7×	`div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `flip3-+` `neg-log` `associate-*l/` `frac-add` `associate-/r/` `associate-+l-` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 139

Calls

4 calls:

17.0ms	(+ (- (* (/ (cos B) (/ (sin B) x)) 1.0)) (/ 1.0 (sin B)))
4.0ms	(/ 1.0 (sin B))
6.0ms	(/ (sin B) x)
11.0ms	(/ (cos B) (/ (sin B) x))

series382.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(+ (- (* (/ (cos B) (/ (sin B) x)) 1.0)) (/ 1.0 (sin B)))
23.0ms	(/ 1.0 (sin B))
44.0ms	(/ (sin B) x)
110.0ms	(/ (cos B) (/ (sin B) x))

simplify1.4s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	3184
1	654
0	260

prune972.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes151.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.1s	1680×	body	1280	valid
1.5s	1489×	body	640	valid
1.1s	4898×	body	80	valid
854.0ms	718×	body	320	valid
113.0ms	344×	body	160	valid