Details

sample494.0ms

Algorithm

intervals

Results

231.0ms	81×	body	1280	valid
147.0ms	74×	body	640	valid
59.0ms	73×	body	80	valid
20.0ms	17×	body	320	valid
9.0ms	11×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2752
3	622
2	177
1	74
0	32

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize101.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.1b	(- (cos x) (cos y))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg`
5×	`sqrt-prod`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 98

Calls

4 calls:

71.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
40.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
6.0ms	(- (cos x) (cos y))

series337.0ms

Counts

4 → 10

Calls

4 calls:

168.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
105.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
64.0ms	(- (cos x) (cos y))

simplify1.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
2	2113
1	657
0	245

prune856.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize109.0ms

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))) (- (cos x) (cos y)))
0.4b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.1b	(- (cos x) (cos y))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-*r/`
35×	`flip3--` `flip--`
32×	`frac-times`
27×	`add-sqr-sqrt`
20×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`associate-r`
17×	`*-un-lft-identity`
16×	`associate-*l/`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt`
8×	`associate-l`
7×	`sub-neg`
6×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp` `difference-of-squares`
4×	`sqrt-prod` `insert-posit16` `distribute-lft-out--`
3×	`*-commutative`
2×	`times-frac` `diff-cos` `unswap-sqr`
1×	`diff-log`

Counts

4 → 137

Calls

4 calls:

288.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
90.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
30.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms	(- (cos x) (cos y))

series697.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
184.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
133.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
64.0ms	(- (cos x) (cos y))

simplify2.4s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	4018
1	894
0	276

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize157.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
0.4b	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
2.1b	(- (cos x) (cos y))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

62×	`associate-*r/`
35×	`flip3--` `flip--`
32×	`frac-times` `pow1` `add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
18×	`add-sqr-sqrt`
16×	`associate-*l/`
15×	`*-un-lft-identity`
13×	`associate-r`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`associate-l`
9×	`sub-neg` `add-cube-cbrt` `sqrt-prod`
6×	`add-log-exp`
4×	`insert-posit16` `difference-of-squares`
3×	`*-commutative` `distribute-lft-out--`
2×	`diff-cos`
1×	`times-frac` `diff-log`

Counts

4 → 146

Calls

4 calls:

803.0ms	(* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
93.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
237.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
9.0ms	(- (cos x) (cos y))

series743.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
131.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
181.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
73.0ms	(- (cos x) (cos y))

simplify3.6s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	4443
1	933
0	290

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize124.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (sin y) (/ (sin x) 16.0)) (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (- (* (cos x) (cos x)) (* (cos y) (cos y)))))
0.4b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
0.5b	(+ (cos x) (cos y))
2.2b	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

rewrite497.0ms

Algorithm

rewrite-expression-head

Rules

52×	`frac-times`
41×	`flip3--` `flip--`
40×	`associate-*l/` `cos-mult`
26×	`associate-*r/`
22×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
10×	`frac-sub` `sub-div`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`sqr-cos`
5×	`sub-neg` `associate--l+` `difference-of-squares`
4×	`sqrt-prod` `insert-posit16`
2×	`times-frac` `*-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `sum-cos` `diff-log` `flip-+` `distribute-lft-out` `associate--r+`

Counts

4 → 141

Calls

4 calls:

425.0ms	(* (- (sin y) (/ (sin x) 16.0)) (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (- (* (cos x) (cos x)) (* (cos y) (cos y)))))
39.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
13.0ms	(+ (cos x) (cos y))
18.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(* (- (sin y) (/ (sin x) 16.0)) (* (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (- (* (cos x) (cos x)) (* (cos y) (cos y)))))
140.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
77.0ms	(+ (cos x) (cos y))
102.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

simplify3.5s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	4995
1	1009
0	342

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

regimes364.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	50
1	50
0	39

end0.0ms

sample18.6s

Algorithm

intervals

Results

9.4s	2667×	body	1280	valid
5.5s	1777×	body	640	valid
1.7s	758×	body	320	valid
1.3s	2433×	body	80	valid
349.0ms	365×	body	160	valid