Details

sample328.0ms

Algorithm

intervals

Results

124.0ms	56×	body	640	valid
57.0ms	44×	body	1280	valid
33.0ms	163×	body	80	valid
19.0ms	26×	body	320	valid
5.0ms	12×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	11
3	39	11
4	50	11
5	53	11
done	53	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

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:

32.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
11.0ms	(/ 1.0 (sin B))
9.0ms	(/ 1.0 (tan B))
43.0ms	(* x (/ 1.0 (tan B)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
44.0ms	(/ 1.0 (sin B))
76.0ms	(/ 1.0 (tan B))
247.0ms	(* x (/ 1.0 (tan B)))

simplify1.5s

Counts

115 → 115

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	180	1184
1	443	1129
2	1636	1030
done	5000	1023

prune957.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
0.1b	(* x (cos B))
0.2b	(/ 1 (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

61.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
18.0ms	(* x (cos B))
14.0ms	(/ 1 (sin B))
36.0ms	(/ (* x (cos B)) (sin B))

series462.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
66.0ms	(* x (cos B))
29.0ms	(/ 1 (sin B))
189.0ms	(/ (* x (cos B)) (sin B))

simplify4.1s

Counts

104 → 104

Iterations

Useful iterations: 2 (362.0ms)

Iter	Nodes	Cost
0	145	1077
1	327	981
2	1794	905
done	5000	905

prune630.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 107

Calls

4 calls:

12.0ms	(/ 1.0 (sin B))
12.0ms	(/ 1.0 (sin B))
71.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
33.0ms	(* x (/ 1.0 (sin B)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (sin B))
40.0ms	(/ 1.0 (sin B))
205.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
105.0ms	(* x (/ 1.0 (sin B)))

simplify1.7s

Counts

119 → 119

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	134	1140
1	336	1101
2	1618	973
done	5000	965

prune853.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

36.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))

series792.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
192.0ms	(cbrt (sin B))
188.0ms	(cbrt (sin B))
179.0ms	(cbrt (sin B))

simplify1.7s

Counts

85 → 85

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	75	710
1	177	628
2	754	534
done	5000	520

prune609.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes258.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
done	15	14

end0.0ms

sample7.5s

Algorithm

intervals

Results

2.7s	1765×	body	1280	valid
1.9s	1416×	body	640	valid
1.7s	4931×	body	80	valid
525.0ms	715×	body	320	valid
132.0ms	350×	body	160	valid