Details

sample398.0ms

Algorithm

intervals

Results

181.0ms	87×	body	1280	valid
79.0ms	82×	body	80	valid
75.0ms	51×	body	640	valid
28.0ms	28×	body	320	valid
5.0ms	8×	body	160	valid

simplify1.5s

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
3.1b	(- (cos x) (cos y))

rewrite689.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

545.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
106.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms	(- 3.0 (sqrt 5.0))
16.0ms	(- (cos x) (cos y))

series563.0ms

Counts

4 → 10

Calls

4 calls:

311.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
160.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
92.0ms	(- (cos x) (cos y))

simplify2.4s

Counts

125 → 125

Iterations

Useful iterations: 2 (582.0ms)

Iter	Nodes	Cost
0	275	3305
1	841	3169
2	3986	2943
done	5000	2943

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize82.0ms

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)))
0.3b	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.1b	(- (cos x) (cos y))

rewrite762.0ms

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:

171.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
496.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
72.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms	(- (cos x) (cos y))

series798.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
313.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
165.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
107.0ms	(- (cos x) (cos y))

simplify2.7s

Counts

145 → 145

Iterations

Useful iterations: 2 (857.0ms)

Iter	Nodes	Cost
0	268	4154
1	845	3986
2	4235	3669
done	5001	3669

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.6b	(pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3)
3.1b	(- (cos x) (cos y))

rewrite605.0ms

Algorithm

rewrite-expression-head

Rules

56×	`frac-times` `flip3--` `flip--`
54×	`associate-*r/`
52×	`cube-div`
28×	`associate-*l/`
26×	`cbrt-div`
20×	`add-sqr-sqrt`
16×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`cbrt-prod`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`pow-pow` `pow-exp` `sqrt-prod` `rem-cube-cbrt`
3×	`sub-neg` `pow-unpow` `difference-of-squares`
2×	`distribute-rgt-in` `cube-mult` `unpow-prod-down` `distribute-lft-in` `unpow3` `cube-prod` `distribute-lft-out--` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `times-frac` `pow1/3` `diff-log` `*-commutative` `rem-cbrt-cube` `diff-cos`

Counts

4 → 143

Calls

4 calls:

37.0ms	(cbrt (pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3))
69.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
481.0ms	(pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3)
8.0ms	(- (cos x) (cos y))

series2.1s

Counts

4 → 12

Calls

4 calls:

338.0ms	(cbrt (pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3))
128.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.6s	(pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3)
83.0ms	(- (cos x) (cos y))

simplify639.0ms

Counts

155 → 155

Iterations

Useful iterations: done (631.0ms)

Iter	Nodes	Cost
0	357	5833
1	1164	5253
done	5000	5070

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize91.0ms

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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.1b	(- (cos x) (cos y))
3.8b	(log (exp (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))))

rewrite570.0ms

Algorithm

rewrite-expression-head

Rules

29×	`flip3--` `flip--`
28×	`frac-times` `associate-*r/`
22×	`add-sqr-sqrt`
16×	`pow1`
15×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
14×	`associate-*l/`
12×	`associate-r`
9×	`add-cube-cbrt`
7×	`sub-neg` `log-prod` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`exp-sum` `sqrt-prod` `difference-of-squares`
3×	`log-pow` `distribute-lft-out--`
2×	`*-commutative` `diff-cos` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `times-frac` `diff-log` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

463.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
65.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms	(- (cos x) (cos y))
21.0ms	(log (exp (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))))

series1000.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
150.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
109.0ms	(- (cos x) (cos y))
371.0ms	(log (exp (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))))

simplify2.4s

Counts

130 → 130

Iterations

Useful iterations: 2 (605.0ms)

Iter	Nodes	Cost
0	260	3866
1	780	3690
2	3861	3403
done	5002	3403

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes285.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	60
1	49	60
done	49	60

end0.0ms

sample14.4s

Algorithm

intervals

Results

7.5s	2705×	body	1280	valid
4.0s	1806×	body	640	valid
1.4s	765×	body	320	valid
773.0ms	2375×	body	80	valid
299.0ms	349×	body	160	valid