Details

sample436.0ms

Algorithm

intervals

Results

174.0ms	87×	body	1280	valid
122.0ms	29×	body	320	valid
79.0ms	60×	body	640	valid
18.0ms	68×	body	80	valid
8.0ms	12×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	192	47
3	697	47
4	2907	47
done	5001	47

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize65.0ms

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

rewrite129.0ms

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:

13.0ms	(/ (/ (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)))
78.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

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) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
126.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
61.0ms	(- (cos x) (cos y))

simplify2.2s

Counts

260 → 260

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	658	11736
1	1394	10851
2	3895	9139
done	5000	9131

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize63.0ms

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

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

17.0ms	(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (* (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
137.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
18.0ms	(- 3.0 (sqrt 5.0))
13.0ms	(- (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) (* (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
173.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
82.0ms	(- (cos x) (cos y))

simplify2.2s

Counts

211 → 211

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	560	7555
1	1176	6716
2	3493	5006
done	5000	4536

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.5b	(- (cos x) (cos y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt 16.0)
1.0ms	(cbrt 16.0)
1.0ms	(cbrt 16.0)
10.0ms	(- (cos x) (cos y))

series60.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
59.0ms	(- (cos x) (cos y))

simplify1.9s

Counts

74 → 74

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	124	888
1	246	765
2	552	583
3	1846	522
done	5000	513

prune721.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
105×	`prod-diff`
103×	`*-un-lft-identity`
97×	`add-cube-cbrt`
58×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
12×	`add-exp-log`
8×	`add-log-exp`
7×	`pow1` `log-prod` `div-inv`
6×	`fma-neg` `associate-r` `associate-l` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`flip3--` `rem-log-exp` `flip--` `distribute-lft-out--`
2×	`diff-log` `associate-*r/` `div-exp` `prod-exp` `unswap-sqr`
1×	`log-div` `pow-prod-down` `log-pow` `*-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 199

Calls

4 calls:

6.0ms	(log (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (* (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0)))
88.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
10.0ms	(- 3.0 (sqrt 5.0))
14.0ms	(- (cos x) (cos y))

series3.1s

Counts

4 → 10

Calls

4 calls:

2.9s	(log (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (* (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0)))
119.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
86.0ms	(- (cos x) (cos y))

simplify2.7s

Counts

209 → 209

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	557	7328
1	1149	6487
2	3214	4914
done	5000	4162

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes307.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	82
1	46	82
done	46	82

end0.0ms

sample15.9s

Algorithm

intervals

Results

8.7s	2754×	body	1280	valid
3.7s	1882×	body	640	valid
1.9s	772×	body	320	valid
865.0ms	2233×	body	80	valid
227.0ms	359×	body	160	valid