Details

sample471.0ms

Algorithm

intervals

Results

277.0ms	89×	body	1280	valid
92.0ms	57×	body	640	valid
23.0ms	76×	body	80	valid
17.0ms	18×	body	320	valid
15.0ms	16×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3141
3	655
2	181
1	74
0	32

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))) 2.0) (* (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))) 3.0))
0.4b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`add-cbrt-cube` `add-exp-log`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1` `associate-r` `associate-l` `associate-*l/`
5×	`sqrt-prod` `difference-of-squares`
4×	`times-frac` `associate-/r/`
3×	`flip3-+` `flip3--` `flip-+` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `frac-add` `prod-exp` `associate-*r/` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `diff-cos`

Counts

4 → 84

Calls

4 calls:

399.0ms	(/ (+ (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))) 2.0) (* (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))) 3.0))
87.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
10.0ms	(- 3.0 (sqrt 5.0))
8.0ms	(- (cos x) (cos y))

series2.3s

Counts

4 → 10

Calls

4 calls:

2.0s	(/ (+ (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))) 2.0) (* (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))) 3.0))
135.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
102.0ms	(- (cos x) (cos y))

simplify1.6s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	3451
1	863
0	322

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize103.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))
1.3b	(- (cos x) (cos y))
1.3b	(- (cos x) (cos y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `flip--` `distribute-lft-out--`
3×	`diff-cos`
1×	`sqrt-prod`

Counts

4 → 60

Calls

4 calls:

5.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))
16.0ms	(- (cos x) (cos y))
6.0ms	(- (cos x) (cos y))

series246.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
82.0ms	(- (cos x) (cos y))
82.0ms	(- (cos x) (cos y))
82.0ms	(- (cos x) (cos y))

simplify3.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
4	4878
3	1145
2	394
1	157
0	79

prune936.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize117.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (cos x) (cos y)))
1.3b	(- (cos x) (cos y))
1.3b	(- (cos x) (cos y))
1.3b	(- (cos x) (cos y))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
6×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

8.0ms	(cbrt (- (cos x) (cos y)))
12.0ms	(- (cos x) (cos y))
11.0ms	(- (cos x) (cos y))
12.0ms	(- (cos x) (cos y))

series359.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (- (cos x) (cos y)))
72.0ms	(- (cos x) (cos y))
74.0ms	(- (cos x) (cos y))
72.0ms	(- (cos x) (cos y))

simplify902.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1567
2	468
1	180
0	90

prune982.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize115.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- (sin x) (/ (sin y) 16.0)))
0.6b	(cbrt (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`cbrt-prod`
8×	`add-log-exp`
7×	`difference-of-squares`
6×	`add-cube-cbrt`
4×	`pow1` `cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `flip--` `distribute-lft-out--`
2×	`sub-neg` `times-frac` `pow1/3` `diff-log`
1×	`sqrt-prod` `diff-cos`

Counts

4 → 62

Calls

4 calls:

8.0ms	(cbrt (- (sin x) (/ (sin y) 16.0)))
9.0ms	(cbrt (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

series556.0ms

Counts

4 → 10

Calls

4 calls:

258.0ms	(cbrt (- (sin x) (/ (sin y) 16.0)))
219.0ms	(cbrt (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
79.0ms	(- (cos x) (cos y))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	2033
2	713
1	306
0	152

prune875.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes428.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	49
1	49
0	38

end0.0ms

sample15.5s

Algorithm

intervals

Results

8.1s	2660×	body	1280	valid
3.5s	1903×	body	640	valid
2.0s	2284×	body	80	valid
1.0s	792×	body	320	valid
419.0ms	361×	body	160	valid