Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	180×	body	80	valid
3.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	26×	body	640	valid
1.0ms	17×	body	320	valid
0.0ms	2×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	184	6
6	250	6
7	287	6
8	349	6
9	437	6
10	574	6
11	654	6
12	712	6
13	785	6
14	1075	6
15	1150	6
16	1193	6
17	1213	6
18	1221	6
19	1221	6
done	1221	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite228.0ms

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:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
176.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series114.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	335	555
1	1087	529
2	5002	525
done	5002	525

prune218.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.5b

localize9.0ms

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

rewrite841.0ms

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-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

528.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
34.0ms	(/ beta (+ (+ alpha beta) 2.0))
214.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series252.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
85.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify124.0ms

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	977	8429
1	3143	6259
2	5002	6131
done	5002	6131

prune771.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.0b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

346×	`*-un-lft-identity`
189×	`prod-diff`
185×	`add-sqr-sqrt`
170×	`add-cube-cbrt`
168×	`times-frac`
130×	`exp-sum`
102×	`distribute-lft-out`
68×	`log-prod`
22×	`associate-/r/`
21×	`fma-neg`
12×	`exp-prod`
11×	`flip3-+` `flip-+` `div-inv`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 309

Calls

4 calls:

350.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
387.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
211.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series293.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
85.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify79.0ms

Counts

321 → 321

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	638	4268
1	1852	3053
2	5002	2419
done	5002	2419

prune501.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite275.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

211.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
18.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
18.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
18.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series533.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
154.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
147.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
155.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify64.0ms

Counts

209 → 209

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	509	2277
1	1447	1794
2	5001	1714
done	5001	1714

prune687.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

regimes87.0ms

Accuracy

76.8% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.3b

bsearch64.0ms

Steps

Iters	Range		Point
10	7.61445106428951e+17	2.9705373761200776e+32	6.566215071237633e+18

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	27
1	39	27
done	39	27

end0.0ms

sample612.0ms

Algorithm

intervals

Results

136.0ms	5785×	body	80	valid
104.0ms	879×	body	1280	valid
85.0ms	8000×	pre	80	true
72.0ms	741×	body	640	valid
27.0ms	406×	body	320	valid
9.0ms	189×	body	160	valid