Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	191×	body	80	valid
4.0ms	28×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	21×	body	640	valid
1.0ms	10×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite34.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series112.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- 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

prune157.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 14.8b

Counts

72 → 10

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))
0.1b	(/ alpha (+ (+ alpha beta) 2.0))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite65.0ms

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:

32.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series248.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (13.0ms)

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

prune349.0ms

Filtered

149 candidates to 103 candidates (69.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	152	7	159

Merged error: 1.5b

Counts

159 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ alpha (+ (+ alpha beta) 2.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.5b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite95.0ms

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:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
23.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
40.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series307.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
66.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
72.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
116.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify162.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	863	2332
1	4947	2044
2	5001	2044

prune626.0ms

Filtered

262 candidates to 131 candidates (50.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	263	6	269

Merged error: 1.4b

Counts

269 → 6

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))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series392.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (+ (+ alpha beta) 2.0))
103.0ms	(cbrt (+ (+ alpha beta) 2.0))
104.0ms	(cbrt (+ (+ alpha beta) 2.0))
83.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	278	567
1	708	537
2	2658	521
3	5001	512

prune227.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Merged error: 1.4b

Counts

78 → 7

regimes109.0ms

Accuracy

74.2% (3.5b remaining)

Error of 6.7b against oracle of 3.2b and baseline of 16.7b

bsearch69.0ms

Steps

Iters	Range		Point
10	312253337667.5445	1.7481323259708506e+24	340647131676.5717

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	35
1	45	35

end0.0ms

sample621.0ms

Algorithm

intervals

Results

152.0ms	5832×	body	80	valid
106.0ms	834×	body	1280	valid
104.0ms	8000×	pre	80	true
75.0ms	725×	body	640	valid
34.0ms	413×	body	320	valid
10.0ms	196×	body	160	valid