Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	196×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	24×	body	1280	valid
2.0ms	25×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	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: 14.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite217.0ms

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:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
167.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series109.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune199.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite811.0ms

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:

33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
34.0ms	(/ beta (+ (+ alpha beta) 2.0))
509.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
202.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series234.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
66.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify132.0ms

Counts

425 → 425

Iterations

Useful iterations: 2 (72.0ms)

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

prune721.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.6b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
0.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite934.0ms

Algorithm

rewrite-expression-head

Rules

1202×	`*-un-lft-identity`
1020×	`times-frac`
895×	`add-sqr-sqrt`
566×	`add-cube-cbrt`
498×	`prod-diff`
300×	`distribute-lft-out`
131×	`difference-of-squares`
83×	`fma-neg`
69×	`distribute-lft-out--`
65×	`associate--r+`
43×	`div-inv`
22×	`associate-/r*` `associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
8×	`flip3-+` `div-exp` `flip-+` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub` `associate-/l/`
1×	`pow-flip` `inv-pow` `associate--r-`

Counts

4 → 768

Calls

4 calls:

67.0ms	(/ (+ (+ alpha beta) 2.0) beta)
554.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
38.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
205.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series268.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (+ (+ alpha beta) 2.0) beta)
101.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
61.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify169.0ms

Counts

780 → 780

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1499	20817
1	5001	14368
done	5001	14368

prune846.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1) (+ (+ alpha beta) 2.0))
0.0b	(fma (/ (sqrt 1) (+ (+ alpha beta) 2.0)) (/ (sqrt 1) (/ 1 beta)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
0.2b	(/ (sqrt 1) (/ 1 beta))
0.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
232×	`times-frac`
162×	`add-sqr-sqrt`
157×	`add-cube-cbrt`
63×	`prod-diff`
60×	`sqrt-prod`
57×	`distribute-lft-out`
21×	`fma-neg`
18×	`associate-/r*`
15×	`add-exp-log`
13×	`div-inv`
12×	`associate-/l*`
11×	`associate-/r/` `add-cbrt-cube`
7×	`div-exp`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `rec-exp` `flip3--` `diff-log` `1-exp` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 284

Calls

4 calls:

35.0ms	(/ (sqrt 1) (+ (+ alpha beta) 2.0))
0.0ms	(fma (/ (sqrt 1) (+ (+ alpha beta) 2.0)) (/ (sqrt 1) (/ 1 beta)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
12.0ms	(/ (sqrt 1) (/ 1 beta))
205.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series227.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (sqrt 1) (+ (+ alpha beta) 2.0))
102.0ms	(fma (/ (sqrt 1) (+ (+ alpha beta) 2.0)) (/ (sqrt 1) (/ 1 beta)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
9.0ms	(/ (sqrt 1) (/ 1 beta))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify79.0ms

Counts

296 → 296

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	833	2891
1	3369	1946
2	5001	1557
done	5001	1557

prune398.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.8b

regimes52.0ms

Accuracy

76.8% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 16.0b

bsearch70.0ms

Steps

Iters	Range		Point
10	1918684245868153.5	3.072219510867474e+30	6.769387663364106e+18

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35
done	42	35

end0.0ms

sample618.0ms

Algorithm

intervals

Results

136.0ms	5822×	body	80	valid
101.0ms	848×	body	1280	valid
87.0ms	8000×	pre	80	true
65.0ms	716×	body	640	valid
35.0ms	411×	body	320	valid
9.0ms	203×	body	160	valid