Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	191×	body	80	valid
3.0ms	26×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	25×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	6×	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: 15.2b

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)

rewrite192.0ms

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:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
145.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series95.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
55.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune142.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.8b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

942.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
34.0ms	(/ beta (+ (+ alpha beta) 2.0))
32.0ms	(/ alpha (+ (+ alpha beta) 2.0))
169.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
40.0ms	(/ beta (+ (+ alpha beta) 2.0))
43.0ms	(/ alpha (+ (+ alpha beta) 2.0))
65.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5001	1268

prune326.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite603.0ms

Algorithm

rewrite-expression-head

Rules

273×	`*-un-lft-identity`
153×	`times-frac`
139×	`add-sqr-sqrt`
102×	`distribute-lft-out`
81×	`add-cube-cbrt`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
24×	`difference-of-squares`
21×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
14×	`associate-/r/`
12×	`pow1`
11×	`sqr-pow`
7×	`flip3-+` `flip-+` `div-inv`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out--`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `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--`

Counts

4 → 250

Calls

4 calls:

34.0ms	(/ alpha (+ (+ alpha beta) 2.0))
36.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
144.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
376.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series255.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ alpha (+ (+ alpha beta) 2.0))
63.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
55.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
97.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify156.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	863	2332
1	4944	2044
2	5001	2044

prune583.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
1.4b	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

341×	`add-sqr-sqrt`
300×	`*-un-lft-identity`
262×	`unpow-prod-down`
241×	`cube-prod`
185×	`times-frac`
140×	`difference-of-squares`
99×	`distribute-lft-out`
81×	`add-cube-cbrt`
74×	`sqr-pow`
39×	`swap-sqr`
22×	`add-exp-log`
21×	`associate-r` `associate-l` `distribute-lft-out--`
19×	`add-cbrt-cube`
14×	`associate-/r/`
13×	`pow1`
7×	`flip3-+` `flip-+` `div-inv`
6×	`pow-unpow` `div-exp` `add-log-exp`
5×	`cbrt-undiv`
4×	`pow-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `frac-times` `sub-neg` `flip3--` `pow-plus` `diff-log` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 381

Calls

4 calls:

36.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
142.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
36.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
861.0ms	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

series300.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
51.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
84.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
101.0ms	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

393 → 393

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1108	4907
1	5001	4629

prune986.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

regimes148.0ms

Accuracy

99.3% (0.1b remaining)

Error of 3.3b against oracle of 3.3b and baseline of 15.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	30
1	43	30

end0.0ms

sample630.0ms

Algorithm

intervals

Results

144.0ms	5821×	body	80	valid
102.0ms	799×	body	1280	valid
83.0ms	8000×	pre	80	true
76.0ms	756×	body	640	valid
29.0ms	421×	body	320	valid
10.0ms	203×	body	160	valid