Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	194×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	25×	body	1280	valid
2.0ms	22×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify75.0ms

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: 14.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite225.0ms

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))
173.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series112.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
61.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify35.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (28.0ms)

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

prune215.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

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))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite990.0ms

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:

679.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
212.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify121.0ms

Counts

425 → 425

Iterations

Useful iterations: 2 (68.0ms)

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

prune742.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize17.0ms

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))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite270.0ms

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

Counts

4 → 152

Calls

4 calls:

16.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
17.0ms	(cbrt (+ (+ alpha beta) 2.0))
213.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series392.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (+ (+ alpha beta) 2.0))
103.0ms	(cbrt (+ (+ alpha beta) 2.0))
103.0ms	(cbrt (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify51.0ms

Counts

164 → 164

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	460	1755
1	1302	1290
2	5001	1240
done	5001	1240

prune429.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize24.0ms

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))
1.6b	(fma (/ (* (cbrt alpha) (cbrt alpha)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt alpha) (cbrt (+ (+ alpha beta) 2.0))) (- 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
15×	`cbrt-prod`
9×	`distribute-lft-out`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

18.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(cbrt (+ (+ alpha beta) 2.0))
0.0ms	(fma (/ (* (cbrt alpha) (cbrt alpha)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt alpha) (cbrt (+ (+ alpha beta) 2.0))) (- 1.0))

series659.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (+ (+ alpha beta) 2.0))
101.0ms	(cbrt (+ (+ alpha beta) 2.0))
102.0ms	(cbrt (+ (+ alpha beta) 2.0))
354.0ms	(fma (/ (* (cbrt alpha) (cbrt alpha)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt alpha) (cbrt (+ (+ alpha beta) 2.0))) (- 1.0))

simplify101.0ms

Counts

73 → 73

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	332	749
1	965	663
2	4121	636
3	5001	608
done	5001	608

prune364.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.7b

regimes112.0ms

Accuracy

77.4% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.8b

bsearch58.0ms

Steps

Iters	Range		Point
9	388973939020430.44	2.0000525779394545e+23	6665734284871154.0

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	37
1	43	37
done	43	37

end0.0ms

sample617.0ms

Algorithm

intervals

Results

135.0ms	5835×	body	80	valid
99.0ms	868×	body	1280	valid
85.0ms	8000×	pre	80	true
67.0ms	721×	body	640	valid
27.0ms	374×	body	320	valid
9.0ms	202×	body	160	valid