Details

sample448.0ms

Algorithm

intervals

Results

233.0ms	96×	body	1280	valid
117.0ms	45×	body	640	valid
29.0ms	25×	body	320	valid
22.0ms	77×	body	80	valid
7.0ms	13×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
4	3022
3	657
2	188
1	74
0	32

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize97.0ms

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)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite219.0ms

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-cbrt-cube` `add-exp-log`
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:

130.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
56.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms	(- 3.0 (sqrt 5.0))
7.0ms	(- (cos x) (cos y))

series462.0ms

Counts

4 → 10

Calls

4 calls:

201.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
163.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
98.0ms	(- (cos x) (cos y))

simplify2.3s

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	2008
0	738

prune3.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (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 (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.4b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

15.0ms	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (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 (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
58.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
7.0ms	(- 3.0 (sqrt 5.0))
9.0ms	(- (cos x) (cos y))

series1.7s

Counts

4 → 10

Calls

4 calls:

1.4s	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (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 (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
151.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
88.0ms	(- (cos x) (cos y))

simplify2.6s

Counts

178 → 178

Iterations

Iter	Nodes
done	5002
2	2981
1	1036
0	438

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y)))) (* (- (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 (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 175

Calls

4 calls:

13.0ms	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y)))) (* (- (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 (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
29.0ms	(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
7.0ms	(- 3.0 (sqrt 5.0))
7.0ms	(- (cos x) (cos y))

series1.8s

Counts

4 → 10

Calls

4 calls:

1.5s	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y)))) (* (- (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 (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
156.0ms	(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
0.0ms	(- 3.0 (sqrt 5.0))
87.0ms	(- (cos x) (cos y))

simplify3.2s

Counts

185 → 185

Iterations

Iter	Nodes
done	5002
2	3242
1	1073
0	447

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize119.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.3b	(* (sqrt 2.0) (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))))
1.0b	(- 3.0 (sqrt 5.0))
1.5b	(- (cos x) (cos y))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

210×	`add-sqr-sqrt`
208×	`*-un-lft-identity`
204×	`add-cube-cbrt`
183×	`times-frac` `prod-diff`
164×	`distribute-rgt-in` `distribute-lft-in`
18×	`add-exp-log`
17×	`div-inv`
14×	`add-cbrt-cube`
13×	`sqrt-prod` `associate-/l*`
10×	`associate-*r/`
9×	`pow1`
8×	`flip3--` `flip--` `add-log-exp`
6×	`sub-neg` `fma-neg` `div-exp` `associate-l`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `pow-prod-down` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`diff-log` `associate-*l/` `distribute-lft-out--`
1×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-r` `*-commutative` `diff-cos` `associate-/l/`

Counts

4 → 336

Calls

4 calls:

9.0ms	(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
149.0ms	(* (sqrt 2.0) (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))))
7.0ms	(- 3.0 (sqrt 5.0))
7.0ms	(- (cos x) (cos y))

series809.0ms

Counts

4 → 10

Calls

4 calls:

527.0ms	(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
181.0ms	(* (sqrt 2.0) (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))))
0.0ms	(- 3.0 (sqrt 5.0))
101.0ms	(- (cos x) (cos y))

simplify3.6s

Counts

346 → 346

Iterations

Iter	Nodes
done	5000
2	4436
1	1869
0	833

prune3.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes328.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	33
1	33
0	30

end0.0ms

sample15.1s

Algorithm

intervals

Results

8.4s	2773×	body	1280	valid
3.3s	1833×	body	640	valid
1.9s	800×	body	320	valid
891.0ms	2229×	body	80	valid
290.0ms	365×	body	160	valid