Details

sample307.0ms

Algorithm

intervals

Results

145.0ms	81×	body	1280	valid
89.0ms	49×	body	640	valid
21.0ms	26×	body	320	valid
18.0ms	90×	body	80	valid
4.0ms	10×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	181	50
3	656	50
4	3157	50
done	5000	50

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize60.0ms

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 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
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` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 94

Calls

4 calls:

119.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
82.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms	(- 3.0 (sqrt 5.0))
12.0ms	(- (cos x) (cos y))

series375.0ms

Counts

4 → 10

Calls

4 calls:

202.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
106.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
66.0ms	(- (cos x) (cos y))

simplify1.4s

Counts

104 → 104

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	238	1837
1	646	1782
2	2893	1629
done	5000	1621

prune900.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

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)))
0.3b	(* (* (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)))
2.8b	(- (cos x) (cos y))

rewrite681.0ms

Algorithm

rewrite-expression-head

Rules

36×	`associate-*r/`
35×	`flip3--` `flip--`
32×	`frac-times`
27×	`add-sqr-sqrt`
20×	`pow1` `add-exp-log` `add-cbrt-cube`
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` `distribute-lft-out--`
3×	`*-commutative`
2×	`times-frac` `diff-cos` `unswap-sqr`
1×	`diff-log`

Counts

4 → 133

Calls

4 calls:

453.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
137.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
53.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
26.0ms	(- (cos x) (cos y))

series655.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
188.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
117.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
79.0ms	(- (cos x) (cos y))

simplify539.0ms

Counts

145 → 145

Iterations

Useful iterations: done (531.0ms)

Iter	Nodes	Cost
0	268	4154
1	880	4010
done	5001	3685

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize70.0ms

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 2.0) (- (sin x) (/ (sin y) 16.0)))
0.6b	(+ (cos x) (cos y))
2.8b	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

133.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
79.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
15.0ms	(+ (cos x) (cos y))
30.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
125.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
66.0ms	(+ (cos x) (cos y))
105.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

simplify2.1s

Counts

106 → 106

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	239	1972
1	702	1861
2	3574	1671
done	5000	1663

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize106.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (+ (cos y) (cos x)) 3))
0.5b	(pow (+ (cos y) (cos x)) 3)
0.6b	(+ (cos y) (cos x))
2.8b	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `sum-cos` `add-cbrt-cube` `distribute-lft-out`
4×	`cube-div` `cos-mult`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`cube-mult` `sqr-cos` `cbrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow1/3` `diff-log` `pow-exp` `associate--l+` `sum-log` `frac-sub` `flip--` `rem-cbrt-cube` `associate--r+` `sub-div` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

9.0ms	(cbrt (pow (+ (cos y) (cos x)) 3))
15.0ms	(pow (+ (cos y) (cos x)) 3)
14.0ms	(+ (cos y) (cos x))
34.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cbrt (pow (+ (cos y) (cos x)) 3))
102.0ms	(pow (+ (cos y) (cos x)) 3)
52.0ms	(+ (cos y) (cos x))
118.0ms	(- (* (cos x) (cos x)) (* (cos y) (cos y)))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	150	1332
1	470	1063
2	2585	960
done	5001	959

prune983.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

regimes277.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	72
1	60	72
done	60	72

end0.0ms

sample14.2s

Algorithm

intervals

Results

7.1s	2775×	body	1280	valid
4.1s	1838×	body	640	valid
987.0ms	2292×	body	80	valid
838.0ms	747×	body	320	valid
742.0ms	348×	body	160	valid