Details

sample54.0ms

Algorithm

intervals

Results

13.0ms	256×	pre	80	true
12.0ms	193×	body	80	valid
8.0ms	28×	body	1280	valid
4.0ms	19×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
25	4885
24	4583
23	4303
22	3954
21	3572
20	3229
19	2829
18	2315
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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite353.0ms

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:

85.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
262.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series190.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
104.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify969.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	1170
1	342
0	130

prune343.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 417

Calls

4 calls:

703.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
36.0ms	(/ alpha (+ (+ alpha beta) 2.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
266.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series364.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
73.0ms	(/ alpha (+ (+ alpha beta) 2.0))
75.0ms	(/ beta (+ (+ alpha beta) 2.0))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.6s

Counts

429 → 429

Iterations

Iter	Nodes
done	5003
2	2686
1	995
0	406

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.2b

localize43.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite336.0ms

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:

18.0ms	(cbrt (+ (+ alpha beta) 2.0))
30.0ms	(cbrt (+ (+ alpha beta) 2.0))
19.0ms	(cbrt (+ (+ alpha beta) 2.0))
263.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series561.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (+ (+ alpha beta) 2.0))
157.0ms	(cbrt (+ (+ alpha beta) 2.0))
141.0ms	(cbrt (+ (+ alpha beta) 2.0))
108.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.5s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
3	3887
2	1186
1	472
0	206

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.8b	(pow (+ (+ alpha beta) 2.0) 1/3)

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

142×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
10×	`cbrt-prod`
8×	`associate-/r/`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `unpow-prod-down` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow-unpow`
2×	`pow1/3` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `unpow1/3` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 161

Calls

4 calls:

23.0ms	(cbrt (+ (+ alpha beta) 2.0))
30.0ms	(cbrt (+ (+ alpha beta) 2.0))
254.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

series451.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (+ (+ alpha beta) 2.0))
113.0ms	(cbrt (+ (+ alpha beta) 2.0))
97.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
113.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

simplify3.4s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
3	4756
2	1459
1	561
0	232

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.2b

regimes405.0ms

Accuracy

99% (0.1b remaining)

Error of 3.1b against oracle of 3.0b and baseline of 16.3b

bsearch3.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	33

end0.0ms

sample1.5s

Algorithm

intervals

Results

418.0ms	5837×	body	80	valid
346.0ms	8000×	pre	80	true
271.0ms	831×	body	1280	valid
198.0ms	712×	body	640	valid
67.0ms	410×	body	320	valid
23.0ms	210×	body	160	valid