Details

sample360.0ms

Algorithm

intervals

Results

153.0ms	84×	body	1280	valid
126.0ms	50×	body	640	valid
28.0ms	34×	body	320	valid
19.0ms	75×	body	80	valid
7.0ms	13×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (24.0ms)

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.4b	(- (cos x) (cos y))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-sqr-sqrt`
118×	`*-un-lft-identity`
106×	`add-cube-cbrt`
105×	`prod-diff`
74×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
28×	`associate-l`
17×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`associate-r`
8×	`pow1` `add-log-exp`
7×	`div-inv`
6×	`fma-neg` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `unswap-sqr`
3×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-r/` `pow-prod-down` `-commutative`
1×	`cbrt-undiv` `div-exp` `associate-*l/` `diff-cos`

Counts

4 → 221

Calls

4 calls:

54.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
77.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms	(- 3.0 (sqrt 5.0))
12.0ms	(- (cos x) (cos y))

series305.0ms

Counts

4 → 10

Calls

4 calls:

112.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
119.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
74.0ms	(- (cos x) (cos y))

simplify631.0ms

Counts

231 → 231

Iterations

Useful iterations: done (619.0ms)

Iter	Nodes	Cost
0	536	6391
1	1264	5586
done	5000	4403

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5.0)
1.0b	(cbrt 5.0)
1.4b	(- (cos x) (cos y))
2.0b	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (* (- (sqrt (cbrt 5.0))) (fabs (cbrt 5.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt 5.0)
1.0ms	(cbrt 5.0)
12.0ms	(- (cos x) (cos y))
1.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (* (- (sqrt (cbrt 5.0))) (fabs (cbrt 5.0))))

series76.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(cbrt 5.0)
75.0ms	(- (cos x) (cos y))
0.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (* (- (sqrt (cbrt 5.0))) (fabs (cbrt 5.0))))

simplify768.0ms

Counts

71 → 71

Iterations

Useful iterations: done (765.0ms)

Iter	Nodes	Cost
0	136	1024
1	279	911
2	924	720
done	5000	602

prune759.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5.0)
1.0b	(cbrt 5.0)
1.4b	(- (cos x) (cos y))
2.0b	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (* (- (sqrt (cbrt 5.0))) (fabs (cbrt 5.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt 5.0)
1.0ms	(cbrt 5.0)
9.0ms	(- (cos x) (cos y))
0.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (* (- (sqrt (cbrt 5.0))) (fabs (cbrt 5.0))))

series67.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(cbrt 5.0)
67.0ms	(- (cos x) (cos y))
0.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (* (- (sqrt (cbrt 5.0))) (fabs (cbrt 5.0))))

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	109	817
1	208	704
2	688	540
done	5000	455

prune840.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.4b	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 172

Calls

4 calls:

1.0ms	(cbrt (cos x))
88.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
15.0ms	(- 3.0 (sqrt 5.0))
1.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series383.0ms

Counts

4 → 10

Calls

4 calls:

108.0ms	(cbrt (cos x))
99.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
176.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify2.2s

Counts

182 → 182

Iterations

Useful iterations: 2 (643.0ms)

Iter	Nodes	Cost
0	415	5603
1	921	4921
2	4309	3606
done	5000	3606

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes218.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	45	77
1	60	77
2	63	77
3	64	77
done	64	77

end0.0ms

sample16.2s

Algorithm

intervals

Results

8.3s	2738×	body	1280	valid
5.2s	1829×	body	640	valid
1.0s	761×	body	320	valid
946.0ms	2298×	body	80	valid
295.0ms	374×	body	160	valid