Details

sample43.0ms

Algorithm

intervals

Results

15.0ms	201×	body	80	valid
6.0ms	22×	body	1280	valid
5.0ms	256×	pre	80	true
4.0ms	19×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

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	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
86.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series104.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
61.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune153.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
228.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
101.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series228.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ beta (+ (+ alpha beta) 2.0))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune286.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.2b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
139×	`times-frac`
89×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
8×	`div-exp` `div-inv` `associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`cbrt-undiv` `diff-log`
3×	`sub-neg` `flip3--` `flip--`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub` `associate-/l/` `associate--r+`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow` `associate--r-`

Counts

4 → 179

Calls

4 calls:

267.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
36.0ms	(/ (+ (+ alpha beta) 2.0) beta)
22.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series271.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
27.0ms	(/ (+ (+ alpha beta) 2.0) beta)
58.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	643	1681
1	2882	1442
2	5002	1436

prune312.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.2b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.3b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

359×	`*-un-lft-identity`
255×	`times-frac`
185×	`add-sqr-sqrt`
127×	`add-cube-cbrt`
126×	`distribute-lft-out`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
30×	`add-exp-log`
24×	`add-cbrt-cube` `difference-of-squares`
21×	`associate-r` `associate-l`
19×	`associate-/r*`
13×	`pow1` `associate-/r/`
12×	`div-exp`
11×	`div-inv` `sqr-pow`
8×	`cbrt-undiv`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`distribute-lft-out--`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `pow-flip` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `inv-pow`

Counts

4 → 313

Calls

4 calls:

87.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
21.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
24.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
240.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series299.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
72.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
57.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
110.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1137	2969
1	5001	2489

prune657.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

regimes90.0ms

Accuracy

70.5% (3.8b remaining)

Error of 7.0b against oracle of 3.2b and baseline of 16.1b

bsearch81.0ms

Steps

Iters	Range		Point
9	3.721228267677956e+48	9.335976331147918e+57	3.988530834094386e+48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	44
1	52	44

end0.0ms

sample1.3s

Algorithm

intervals

Results

420.0ms	5774×	body	80	valid
244.0ms	878×	body	1280	valid
180.0ms	754×	body	640	valid
152.0ms	8000×	pre	80	true
65.0ms	377×	body	320	valid
29.0ms	217×	body	160	valid