Details

sample359.0ms

Algorithm

intervals

Results

190.0ms	87×	body	1280	valid
62.0ms	60×	body	640	valid
51.0ms	29×	body	320	valid
14.0ms	68×	body	80	valid
6.0ms	12×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	181	50
3	653	50
4	2664	50
done	5000	50

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`associate-l`
20×	`times-frac`
18×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`associate-r`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`distribute-lft-out--`
4×	`sub-neg` `unswap-sqr`
3×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-r/` `pow-prod-down` `-commutative`
1×	`cbrt-undiv` `div-exp` `associate-*l/` `div-inv` `diff-cos`

Counts

4 → 102

Calls

4 calls:

84.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
98.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
26.0ms	(- 3.0 (sqrt 5.0))
16.0ms	(- (cos x) (cos y))

series312.0ms

Counts

4 → 10

Calls

4 calls:

133.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
99.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
79.0ms	(- (cos x) (cos y))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	247	1369
1	584	1330
2	1689	1232
done	5000	1221

prune969.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`sqrt-prod`
11×	`difference-of-squares`
10×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`sub-neg` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `unswap-sqr`
1×	`times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 81

Calls

4 calls:

79.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
27.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
12.0ms	(- 3.0 (sqrt 5.0))
8.0ms	(- (cos x) (cos y))

series226.0ms

Counts

4 → 8

Calls

4 calls:

134.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
0.0ms	(- 3.0 (sqrt 5.0))
92.0ms	(- (cos x) (cos y))

simplify1.6s

Counts

89 → 89

Iterations

Useful iterations: 3 (840.0ms)

Iter	Nodes	Cost
0	182	1026
1	386	981
2	992	919
3	2581	912
done	5000	912

prune742.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))
3.0b	(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`add-log-exp`
9×	`difference-of-squares`
7×	`log-prod`
5×	`pow1` `add-cube-cbrt` `sub-neg`
4×	`add-exp-log` `exp-sum` `add-cbrt-cube` `distribute-lft-out--`
3×	`flip3--` `diff-log` `log-pow` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `diff-cos`

Counts

4 → 68

Calls

4 calls:

24.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
10.0ms	(- 3.0 (sqrt 5.0))
23.0ms	(- (cos x) (cos y))
10.0ms	(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

series195.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(- (sqrt (sqrt 5.0)) (sqrt 1.0))
0.0ms	(- 3.0 (sqrt 5.0))
81.0ms	(- (cos x) (cos y))
114.0ms	(log (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))

simplify2.2s

Counts

76 → 76

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	160	899
1	303	822
2	632	761
3	1424	754
4	4133	751
done	5000	751

prune918.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.5b	(- (cos x) (cos y))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
15×	`associate-r`
13×	`pow1`
11×	`difference-of-squares`
10×	`associate-*r/`
8×	`flip3--` `flip--`
7×	`sqrt-prod`
6×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `pow-prod-down`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `unswap-sqr`
3×	`associate-l/` `-commutative`
1×	`cbrt-undiv` `diff-log` `div-exp` `div-inv` `diff-cos`

Counts

4 → 120

Calls

4 calls:

101.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
40.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
51.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
16.0ms	(- (cos x) (cos y))

series442.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
111.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
101.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
64.0ms	(- (cos x) (cos y))

simplify1.4s

Counts

132 → 132

Iterations

Useful iterations: 2 (382.0ms)

Iter	Nodes	Cost
0	284	2218
1	750	2147
2	2674	1958
done	5002	1958

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes301.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	65
1	48	65
done	48	65

end0.0ms

sample16.9s

Algorithm

intervals

Results

9.3s	2754×	body	1280	valid
4.9s	1882×	body	640	valid
1.2s	772×	body	320	valid
848.0ms	2233×	body	80	valid
234.0ms	359×	body	160	valid