Details

sample298.0ms

Algorithm

intervals

Results

153.0ms	81×	body	1280	valid
62.0ms	71×	body	640	valid
38.0ms	26×	body	320	valid
15.0ms	72×	body	80	valid
3.0ms	6×	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: 0.5b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

138.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
76.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms	(- 3.0 (sqrt 5.0))
17.0ms	(- (cos x) (cos y))

series2.1s

Counts

4 → 10

Calls

4 calls:

1.9s	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
124.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
74.0ms	(- (cos x) (cos y))

simplify2.4s

Counts

98 → 98

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	311	2970
1	875	2901
2	3891	2547
done	5000	2545

prune892.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
2.0b	(- (cos x) (cos y))
2.0b	(- (cos x) (cos y))
2.0b	(- (cos x) (cos y))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

7.0ms	(- 3.0 (sqrt 5.0))
12.0ms	(- (cos x) (cos y))
14.0ms	(- (cos x) (cos y))
10.0ms	(- (cos x) (cos y))

series250.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
84.0ms	(- (cos x) (cos y))
89.0ms	(- (cos x) (cos y))
78.0ms	(- (cos x) (cos y))

simplify983.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (411.0ms)

Iter	Nodes	Cost
0	102	697
1	220	676
2	597	638
3	2291	630
done	5002	630

prune852.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

58.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms	(- (cos x) (cos y))
7.0ms	(- (cos x) (cos y))
8.0ms	(- (cos x) (cos y))

series343.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
86.0ms	(- (cos x) (cos y))
68.0ms	(- (cos x) (cos y))
79.0ms	(- (cos x) (cos y))

simplify774.0ms

Counts

88 → 88

Iterations

Useful iterations: done (772.0ms)

Iter	Nodes	Cost
0	123	986
1	281	965
2	1013	901
done	5000	890

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.0b	(- (cos x) (cos y))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-exp-log`
26×	`times-frac`
23×	`associate-r`
21×	`add-cube-cbrt`
19×	`associate-l`
18×	`add-cbrt-cube`
9×	`prod-exp`
8×	`pow1` `div-exp` `add-log-exp` `unswap-sqr`
5×	`sqrt-prod` `cbrt-unprod` `difference-of-squares`
4×	`cbrt-undiv` `sub-neg` `associate-/r/`
3×	`flip3--` `associate-r/` `associate-l/` `flip--` `distribute-lft-out--`
2×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `flip3-+` `diff-log` `1-exp` `pow-prod-down` `frac-add` `*-commutative` `flip-+` `div-inv`
1×	`frac-times` `diff-cos`

Counts

4 → 121

Calls

4 calls:

138.0ms	(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
108.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms	(- 3.0 (sqrt 5.0))
14.0ms	(- (cos x) (cos y))

series2.4s

Counts

4 → 10

Calls

4 calls:

2.1s	(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
136.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
80.0ms	(- (cos x) (cos y))

simplify726.0ms

Counts

131 → 131

Iterations

Useful iterations: done (712.0ms)

Iter	Nodes	Cost
0	370	5183
1	1091	5096
done	5001	4436

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes472.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	57
1	48	57
done	48	57

end0.0ms

sample14.9s

Algorithm

intervals

Results

7.7s	2747×	body	1280	valid
4.2s	1847×	body	640	valid
1.3s	2293×	body	80	valid
956.0ms	744×	body	320	valid
330.0ms	369×	body	160	valid