Details

sample439.0ms

Algorithm

intervals

Results

183.0ms	87×	body	1280	valid
101.0ms	64×	body	640	valid
72.0ms	65×	body	80	valid
31.0ms	30×	body	320	valid
6.0ms	10×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (108.0ms)

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

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize99.0ms

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

rewrite184.0ms

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:

21.0ms	(/ (/ (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)))
114.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
14.0ms	(- 3.0 (sqrt 5.0))
14.0ms	(- (cos x) (cos y))

series1.7s

Counts

4 → 10

Calls

4 calls:

1.5s	(/ (/ (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)))
147.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
91.0ms	(- (cos x) (cos y))

simplify1.0s

Counts

260 → 260

Iterations

Useful iterations: done (983.0ms)

Iter	Nodes	Cost
0	658	11736
1	1570	10876
done	5000	9459

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.0b	(- (cos x) (cos y))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

184×	`add-sqr-sqrt`
183×	`prod-diff`
172×	`*-un-lft-identity`
164×	`add-cube-cbrt`
110×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
12×	`associate-r` `div-inv`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg` `fma-neg`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
2×	`diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 291

Calls

4 calls:

171.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
97.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms	(- 3.0 (sqrt 5.0))
13.0ms	(- (cos x) (cos y))

series412.0ms

Counts

4 → 10

Calls

4 calls:

195.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
132.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
84.0ms	(- (cos x) (cos y))

simplify1.2s

Counts

301 → 301

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	735	12255
1	2005	10968
done	5000	9307

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (- (sin y) (/ (sin x) 16.0)) 3)
1.0b	(- 3.0 (sqrt 5.0))
1.0b	(- (cos x) (cos y))
7.6b	(cbrt (* (* (pow (- (sin x) (/ (sin y) 16.0)) 3) (* 2.0 (sqrt 2.0))) (pow (- (sin y) (/ (sin x) 16.0)) 3)))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
27×	`add-cube-cbrt` `prod-diff`
14×	`cube-div`
10×	`sqrt-prod`
9×	`flip3--` `flip--`
8×	`cbrt-div` `associate-*l/` `add-log-exp`
7×	`difference-of-squares`
6×	`unpow-prod-down` `fma-neg` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-unpow`
2×	`sub-neg` `times-frac` `diff-log` `associate-*r/` `pow-prod-down`
1×	`cbrt-prod` `cube-mult` `pow-to-exp` `pow-pow` `pow1/3` `unpow3` `pow3` `pow-exp` `rem-cbrt-cube` `diff-cos` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

39.0ms	(pow (- (sin y) (/ (sin x) 16.0)) 3)
15.0ms	(- 3.0 (sqrt 5.0))
16.0ms	(- (cos x) (cos y))
300.0ms	(cbrt (* (* (pow (- (sin x) (/ (sin y) 16.0)) 3) (* 2.0 (sqrt 2.0))) (pow (- (sin y) (/ (sin x) 16.0)) 3)))

series1.0s

Counts

4 → 10

Calls

4 calls:

128.0ms	(pow (- (sin y) (/ (sin x) 16.0)) 3)
0.0ms	(- 3.0 (sqrt 5.0))
90.0ms	(- (cos x) (cos y))
827.0ms	(cbrt (* (* (pow (- (sin x) (/ (sin y) 16.0)) 3) (* 2.0 (sqrt 2.0))) (pow (- (sin y) (/ (sin x) 16.0)) 3)))

simplify2.4s

Counts

130 → 130

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	320	2684
1	900	2254
2	3803	1960
done	5001	1959

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize124.0ms

Local error

Found 4 expressions with local error:

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

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

119×	`add-sqr-sqrt`
114×	`prod-diff`
110×	`*-un-lft-identity`
102×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
10×	`add-log-exp`
9×	`fma-neg`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `div-inv` `difference-of-squares`
5×	`sub-neg`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`diff-log`
2×	`associate-*r/` `diff-cos` `unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 207

Calls

4 calls:

109.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
32.0ms	(- 3.0 (sqrt 5.0))
18.0ms	(- (cos x) (cos y))
17.0ms	(- (cos x) (cos y))

series330.0ms

Counts

4 → 10

Calls

4 calls:

147.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
92.0ms	(- (cos x) (cos y))
90.0ms	(- (cos x) (cos y))

simplify3.5s

Counts

217 → 217

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	455	6319
1	1031	5420
2	4677	4019
done	5000	4019

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes429.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	57
1	47	57
done	47	57

end0.0ms

sample19.8s

Algorithm

intervals

Results

12.6s	2793×	body	1280	valid
3.9s	1802×	body	640	valid
1.1s	752×	body	320	valid
1.1s	2310×	body	80	valid
427.0ms	343×	body	160	valid