Details

sample411.0ms

Algorithm

intervals

Results

201.0ms	89×	body	1280	valid
80.0ms	30×	body	320	valid
73.0ms	59×	body	640	valid
17.0ms	68×	body	80	valid
6.0ms	10×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	192	47
3	699	47
4	3390	47
done	5001	47

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 250

Calls

4 calls:

12.0ms	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
85.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
19.0ms	(- (cos x) (cos y))
9.0ms	(- 3.0 (sqrt 5.0))

series1.3s

Counts

4 → 10

Calls

4 calls:

1.2s	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
94.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
66.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify1.1s

Counts

260 → 260

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	658	11736
1	1570	10876
done	5001	9459

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))
3.2b	(/ (* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0)) (+ (sin x) (/ (sin y) 16.0)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`prod-diff`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`pow1` `fma-neg` `associate-r`
4×	`expm1-log1p-u` `flip3--` `times-frac` `associate-l/` `associate-/r` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`unpow-prod-down` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `diff-cos` `associate-/l` `unpow2` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

73.0ms	(* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0))
15.0ms	(- (cos x) (cos y))
9.0ms	(- 3.0 (sqrt 5.0))
105.0ms	(/ (* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0)) (+ (sin x) (/ (sin y) 16.0)))

series454.0ms

Counts

4 → 10

Calls

4 calls:

151.0ms	(* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0))
64.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))
239.0ms	(/ (* (- (pow (sin x) 2) (* (/ (sin y) 16.0) (/ (sin y) 16.0))) (sqrt 2.0)) (+ (sin x) (/ (sin y) 16.0)))

simplify1.7s

Counts

136 → 136

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	301	2933
1	734	2546
2	3284	2078
done	5002	2036

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
131×	`add-cube-cbrt`
126×	`times-frac`
105×	`prod-diff`
49×	`associate-r`
41×	`distribute-rgt-in` `distribute-lft-in`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`sqrt-prod`
10×	`div-inv`
9×	`associate-l`
8×	`pow1` `add-log-exp`
6×	`fma-neg` `div-exp` `prod-exp` `unswap-sqr`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `associate-*r/` `flip--` `distribute-lft-out--`
2×	`diff-log` `pow-prod-down` `*-commutative`
1×	`rec-exp` `1-exp` `diff-cos`

Counts

4 → 248

Calls

4 calls:

66.0ms	(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))))
131.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(- (cos x) (cos y))
17.0ms	(- 3.0 (sqrt 5.0))

series1.6s

Counts

4 → 10

Calls

4 calls:

1.4s	(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))))
141.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
104.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify1.1s

Counts

258 → 258

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	666	10272
1	1712	9335
done	5001	7810

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize110.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
10×	`sqrt-prod`
9×	`cbrt-prod`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 77

Calls

4 calls:

11.0ms	(- 3.0 (sqrt 5.0))
2.0ms	(cbrt 16.0)
2.0ms	(cbrt 16.0)
19.0ms	(cbrt 16.0)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)

simplify2.2s

Counts

81 → 81

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	123	1173
1	249	961
2	684	763
3	3558	630
done	5000	629

prune954.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes259.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	93
1	56	93
done	56	93

end0.0ms

sample14.8s

Algorithm

intervals

Results

7.8s	2728×	body	1280	valid
4.5s	1838×	body	640	valid
1.1s	737×	body	320	valid
811.0ms	2322×	body	80	valid
276.0ms	375×	body	160	valid