Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	180×	body	80	valid
4.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	25×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	5×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- 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:

23.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
87.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series104.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune138.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.9b

localize10.0ms

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))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite356.0ms

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:

222.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
94.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series230.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ 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

prune261.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* beta (/ 1 (+ (+ alpha beta) 2.0))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.1b	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
33×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
15×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`associate-/r*`
4×	`flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--`
3×	`sub-neg` `associate-r/` `div-exp` `associate-l` `un-div-inv` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `cbrt-unprod` `flip-+` `div-inv` `associate--r+` `difference-of-squares`
1×	`rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `clear-num` `*-commutative` `distribute-lft-out--` `associate--r-`

Counts

4 → 116

Calls

4 calls:

97.0ms	(- (* beta (/ 1 (+ (+ alpha beta) 2.0))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
41.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series223.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* beta (/ 1 (+ (+ alpha beta) 2.0))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	565	957
1	2307	897
2	5001	872

prune252.0ms

Filtered

128 candidates to 85 candidates (66.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite99.0ms

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:

0.0ms	(cbrt beta)
0.0ms	(cbrt beta)
1.0ms	(cbrt beta)
97.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series632.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt beta)
189.0ms	(cbrt beta)
184.0ms	(cbrt beta)
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (40.0ms)

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

prune172.0ms

Filtered

60 candidates to 50 candidates (83.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

regimes63.0ms

Accuracy

75.1% (3.2b remaining)

Error of 6.1b against oracle of 2.9b and baseline of 15.8b

bsearch17.0ms

Steps

Iters	Range		Point
3	35727942855918572.0	4.564364949752027e+16	3.73426938437445e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	26
1	44	26

end0.0ms

sample592.0ms

Algorithm

intervals

Results

142.0ms	5851×	body	80	valid
105.0ms	859×	body	1280	valid
95.0ms	8000×	pre	80	true
73.0ms	741×	body	640	valid
26.0ms	373×	body	320	valid
9.0ms	176×	body	160	valid