Details

sample32.0ms

Algorithm

intervals

Results

7.0ms	191×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	24×	body	1280	valid
3.0ms	23×	body	640	valid
2.0ms	16×	body	320	valid
0.0ms	2×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	53	13
4	74	13
5	163	13
6	314	13
7	647	13
8	1463	13
9	4388	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
245.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series140.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
82.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify962.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (216.0ms)

Iter	Nodes	Cost
0	128	1178
1	341	1110
2	1440	1056
done	5000	1056

prune317.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 229

Calls

4 calls:

1.6s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
300.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series352.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(/ beta (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

241 → 241

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	308	5116
1	742	4394
2	2985	3980
done	5001	3842

prune663.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
36×	`distribute-lft-out`
21×	`fma-neg`
9×	`cbrt-prod`
8×	`associate-/r/`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
261.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series903.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt beta)
255.0ms	(cbrt beta)
278.0ms	(cbrt beta)
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify794.0ms

Counts

152 → 152

Iterations

Useful iterations: done (788.0ms)

Iter	Nodes	Cost
0	177	2800
1	401	2172
2	1223	1862
done	5001	1687

prune751.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.9b	(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
6.9b	(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
142×	`add-sqr-sqrt`
126×	`prod-diff`
124×	`times-frac`
120×	`add-cube-cbrt`
72×	`distribute-lft-out`
42×	`fma-neg`
16×	`associate-/r/`
14×	`sqrt-prod`
8×	`flip3-+` `sqrt-div` `flip-+` `div-inv` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`pow1` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 248

Calls

4 calls:

284.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
339.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.1s	(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.1s	(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
109.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
422.0ms	(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
408.0ms	(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.7s

Counts

260 → 260

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	228	6826
1	559	5432
2	2037	4828
done	5001	4514

prune777.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.0b

regimes147.0ms

Accuracy

99.2% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 16.5b

bsearch2.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	87
1	37	87
done	37	87

end0.0ms

sample1.5s

Algorithm

intervals

Results

335.0ms	5793×	body	80	valid
310.0ms	893×	body	1280	valid
244.0ms	8000×	pre	80	true
189.0ms	713×	body	640	valid
108.0ms	415×	body	320	valid
18.0ms	186×	body	160	valid