Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	183×	body	80	valid
7.0ms	256×	pre	80	true
6.0ms	23×	body	1280	valid
6.0ms	25×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
18	2002
17	1985
16	1722
15	1474
14	1236
13	995
12	795
11	669
10	582
9	467
8	348
7	290
6	209
5	124
4	69
3	50
2	33
1	20
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite262.0ms

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-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 102

Calls

2 calls:

60.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
198.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series172.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
89.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	2016
3	2016
2	1170
1	342
0	130

prune910.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.5b

localize22.0ms

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)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

514×	`*-un-lft-identity`
350×	`add-sqr-sqrt`
273×	`times-frac`
252×	`prod-diff`
215×	`add-cube-cbrt`
138×	`distribute-lft-out`
65×	`associate--r+`
54×	`difference-of-squares`
42×	`fma-neg`
37×	`distribute-lft-out--`
30×	`associate-/r/`
16×	`div-inv`
15×	`flip3-+` `flip-+`
11×	`add-log-exp`
10×	`associate-/l*`
8×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `diff-log` `frac-sub` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`sub-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`div-sub` `associate--r-`

Counts

4 → 428

Calls

4 calls:

938.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
22.0ms	(/ alpha (+ (+ alpha beta) 2.0))
493.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
174.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series319.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
68.0ms	(/ alpha (+ (+ alpha beta) 2.0))
80.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

440 → 440

Iterations

Iter	Nodes
done	2003
2	2003
1	1121
0	456

prune5.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

localize57.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 201

Calls

4 calls:

179.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series750.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
207.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
214.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
230.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.1s

Counts

213 → 213

Iterations

Iter	Nodes
done	2012
3	2012
2	1334
1	523
0	243

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize66.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 156

Calls

4 calls:

19.0ms	(cbrt (+ (+ alpha beta) 2.0))
20.0ms	(cbrt (+ (+ alpha beta) 2.0))
19.0ms	(cbrt (+ (+ alpha beta) 2.0))
234.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series476.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (+ (+ alpha beta) 2.0))
112.0ms	(cbrt (+ (+ alpha beta) 2.0))
131.0ms	(cbrt (+ (+ alpha beta) 2.0))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	2003
3	2003
2	1186
1	472
0	206

prune2.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

regimes177.0ms

Accuracy

73.1% (3.4b remaining)

Error of 6.4b against oracle of 3.0b and baseline of 15.7b

bsearch73.0ms

Steps

Iters	Range		Point
6	2.0302490555836575e+26	1.0361079584824738e+27	2.1159100932126255e+26

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	36

end0.0ms

sample2.3s

Algorithm

intervals

Results

655.0ms	5837×	body	80	valid
423.0ms	873×	body	1280	valid
398.0ms	384×	body	320	valid
351.0ms	8000×	pre	80	true
230.0ms	679×	body	640	valid
38.0ms	227×	body	160	valid