Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	194×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	9×	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: 14.5b

localize8.0ms

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)

rewrite29.0ms

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
17.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series114.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- 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

prune159.0ms

Pruning

14 alts after pruning (14 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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite58.0ms

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:

29.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (37.0ms)

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

prune285.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.3b

localize16.0ms

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)

rewrite29.0ms

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))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series369.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
97.0ms	(cbrt (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

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

prune270.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series622.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt beta)
179.0ms	(cbrt beta)
185.0ms	(cbrt beta)
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	165	261
1	394	243
2	1370	230
3	5002	228

prune168.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.3b

regimes74.0ms

Accuracy

76.4% (3.1b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 16.2b

bsearch47.0ms

Steps

Iters	Range		Point
8	13.202733199564877	775728.8687199388	759519.7231227644

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms

sample616.0ms

Algorithm

intervals

Results

150.0ms	5806×	body	80	valid
111.0ms	847×	body	1280	valid
99.0ms	8000×	pre	80	true
74.0ms	750×	body	640	valid
28.0ms	384×	body	320	valid
11.0ms	213×	body	160	valid