Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	197×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	27×	body	1280	valid
2.0ms	19×	body	640	valid
0.0ms	8×	body	160	valid
0.0ms	5×	body	320	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: 13.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

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))
18.0ms	(+ (/ (- 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)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune149.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.3b

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	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite61.0ms

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:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
10.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ beta (+ (+ alpha beta) 2.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

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

prune278.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.4b

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite34.0ms

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))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series376.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
103.0ms	(cbrt (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify71.0ms

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

prune265.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series341.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	278	573
1	708	539
2	2658	515
3	5001	512

prune288.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

regimes116.0ms

Accuracy

76.4% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 15.9b

bsearch56.0ms

Steps

Iters	Range		Point
10	6953098401.932994	1.5768447876109898e+23	3210135597332015.5

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	24
1	37	24

end0.0ms

sample621.0ms

Algorithm

intervals

Results

150.0ms	5810×	body	80	valid
107.0ms	886×	body	1280	valid
103.0ms	8000×	pre	80	true
67.0ms	708×	body	640	valid
28.0ms	385×	body	320	valid
10.0ms	211×	body	160	valid