Details

sample709.0ms

Algorithm

intervals

Results

362.0ms	92×	body	1280	valid
158.0ms	49×	body	640	valid
42.0ms	79×	body	80	valid
33.0ms	18×	body	320	valid
21.0ms	18×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
4	3171
3	697
2	192
1	74
0	32

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize94.0ms

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)))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
105×	`prod-diff`
103×	`*-un-lft-identity`
97×	`add-cube-cbrt`
58×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`div-inv`
6×	`pow1` `fma-neg` `associate-r` `associate-l` `associate-*r/`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip3--` `flip-+` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `diff-log` `div-exp` `associate-*l/` `frac-add` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative` `diff-cos`

Counts

4 → 211

Calls

4 calls:

71.0ms	(/ (+ 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)))))
56.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms	(- (cos x) (cos y))
5.0ms	(- 3.0 (sqrt 5.0))

series2.2s

Counts

4 → 10

Calls

4 calls:

2.0s	(/ (+ 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)))
65.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify1.8s

Counts

221 → 221

Iterations

Iter	Nodes
done	5002
1	1614
0	619

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize157.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
45×	`prod-diff`
38×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
10×	`sqrt-prod`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`diff-cos`

Counts

4 → 129

Calls

4 calls:

14.0ms	(- (cos x) (cos y))
14.0ms	(- (cos x) (cos y))
22.0ms	(- (cos x) (cos y))
11.0ms	(- 3.0 (sqrt 5.0))

series245.0ms

Counts

4 → 10

Calls

4 calls:

78.0ms	(- (cos x) (cos y))
80.0ms	(- (cos x) (cos y))
86.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify3.0s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	4638
2	1098
1	404
0	181

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize204.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3)
0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`flip3--` `flip--`
28×	`frac-times`
27×	`prod-diff`
26×	`cube-div` `associate-*r/` `add-cube-cbrt`
14×	`pow1` `add-cbrt-cube` `associate-*l/` `add-exp-log`
10×	`add-log-exp`
9×	`fma-neg`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `insert-posit16` `log1p-expm1-u` `rem-cube-cbrt`
3×	`pow-unpow` `sub-neg` `diff-log` `diff-cos` `distribute-lft-out--` `difference-of-squares`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 147

Calls

4 calls:

252.0ms	(pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3)
9.0ms	(- (cos x) (cos y))
21.0ms	(- (cos x) (cos y))
14.0ms	(- (cos x) (cos y))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.9s	(pow (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) 3)
71.0ms	(- (cos x) (cos y))
77.0ms	(- (cos x) (cos y))
71.0ms	(- (cos x) (cos y))

simplify2.4s

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
1	1263
0	272

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize167.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
45×	`prod-diff`
38×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
10×	`sqrt-prod`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`diff-cos`

Counts

4 → 129

Calls

4 calls:

13.0ms	(- (cos x) (cos y))
13.0ms	(- (cos x) (cos y))
14.0ms	(- (cos x) (cos y))
10.0ms	(- 3.0 (sqrt 5.0))

series250.0ms

Counts

4 → 10

Calls

4 calls:

65.0ms	(- (cos x) (cos y))
100.0ms	(- (cos x) (cos y))
84.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify2.5s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	3796
2	1002
1	387
0	175

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes283.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	51
1	51
0	42

end0.0ms

sample20.3s

Algorithm

intervals

Results

11.2s	2739×	body	1280	valid
5.4s	1840×	body	640	valid
1.5s	768×	body	320	valid
1.1s	2302×	body	80	valid
822.0ms	351×	body	160	valid