Details

sample355.0ms

Algorithm

intervals

Results

199.0ms	93×	body	1280	valid
70.0ms	60×	body	640	valid
28.0ms	66×	body	80	valid
23.0ms	28×	body	320	valid
5.0ms	9×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3399
3	699
2	192
1	74
0	32

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize87.0ms

Local error

Found 4 expressions with local error:

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

12.0ms	(/ (/ (fma (* (- (cos x) (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (sqrt 2.0))) (- (sin x) (/ (sin y) 16.0)) 2.0) 3.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) (fma (/ (cos y) 2.0) (- 3.0 (sqrt 5.0)) 1.0)))
50.0ms	(* (- (sin y) (/ (sin x) 16.0)) (sqrt 2.0))
8.0ms	(- 3.0 (sqrt 5.0))
20.0ms	(- (cos x) (cos y))

series1.6s

Counts

4 → 10

Calls

4 calls:

1.4s	(/ (/ (fma (* (- (cos x) (cos y)) (* (- (sin y) (/ (sin x) 16.0)) (sqrt 2.0))) (- (sin x) (/ (sin y) 16.0)) 2.0) 3.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) (fma (/ (cos y) 2.0) (- 3.0 (sqrt 5.0)) 1.0)))
98.0ms	(* (- (sin y) (/ (sin x) 16.0)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
60.0ms	(- (cos x) (cos y))

simplify2.5s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	4707
1	1092
0	448

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize103.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
92×	`add-cube-cbrt`
75×	`times-frac`
63×	`prod-diff`
44×	`distribute-rgt-in` `distribute-lft-in`
18×	`add-exp-log`
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`
5×	`div-inv`
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 → 216

Calls

4 calls:

17.0ms	(/ (/ 1 3.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) (fma (/ (cos y) 2.0) (- 3.0 (sqrt 5.0)) 1.0)))
98.0ms	(* (sqrt 2.0) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))
17.0ms	(- 3.0 (sqrt 5.0))
12.0ms	(- (cos x) (cos y))

series874.0ms

Counts

4 → 10

Calls

4 calls:

578.0ms	(/ (/ 1 3.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) (fma (/ (cos y) 2.0) (- 3.0 (sqrt 5.0)) 1.0)))
208.0ms	(* (sqrt 2.0) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))
0.0ms	(- 3.0 (sqrt 5.0))
87.0ms	(- (cos x) (cos y))

simplify2.7s

Counts

226 → 226

Iterations

Iter	Nodes
done	5000
2	4603
1	1107
0	475

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize126.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt 5.0) (cbrt 5.0))
1.0b	(* (cbrt 5.0) (cbrt 5.0))
1.5b	(- (cos x) (cos y))
61.9b	(fma (- (sqrt (cbrt 5.0))) (sqrt (* (cbrt 5.0) (cbrt 5.0))) (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
32×	`cbrt-prod`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`pow1`
12×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
9×	`prod-diff`
8×	`add-exp-log` `unswap-sqr`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 123

Calls

4 calls:

9.0ms	(* (cbrt 5.0) (cbrt 5.0))
9.0ms	(* (cbrt 5.0) (cbrt 5.0))
7.0ms	(- (cos x) (cos y))
1.0ms	(fma (- (sqrt (cbrt 5.0))) (sqrt (* (cbrt 5.0) (cbrt 5.0))) (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0)))))

series58.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(* (cbrt 5.0) (cbrt 5.0))
0.0ms	(* (cbrt 5.0) (cbrt 5.0))
57.0ms	(- (cos x) (cos y))
0.0ms	(fma (- (sqrt (cbrt 5.0))) (sqrt (* (cbrt 5.0) (cbrt 5.0))) (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0)))))

simplify1.2s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1041
1	279
0	135

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize198.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
14×	`sqrt-prod`
10×	`add-log-exp`
9×	`fma-neg`
6×	`pow1` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`associate-*l/` `diff-cos` `unswap-sqr`
1×	`times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 125

Calls

4 calls:

70.0ms	(* (- (sin y) (/ (sin x) 16.0)) (sqrt 2.0))
7.0ms	(- 3.0 (sqrt 5.0))
7.0ms	(- (cos x) (cos y))
7.0ms	(- (cos x) (cos y))

series338.0ms

Counts

4 → 10

Calls

4 calls:

167.0ms	(* (- (sin y) (/ (sin x) 16.0)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
97.0ms	(- (cos x) (cos y))
74.0ms	(- (cos x) (cos y))

simplify1.7s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1781
1	512
0	235

prune1.6s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes391.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample14.9s

Algorithm

intervals

Results

8.0s	2700×	body	1280	valid
3.8s	1843×	body	640	valid
1.4s	791×	body	320	valid
1.1s	2325×	body	80	valid
344.0ms	341×	body	160	valid