Details

sample34.0ms

Algorithm

intervals

Results

9.0ms	183×	body	80	valid
5.0ms	32×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	26×	body	640	valid
1.0ms	9×	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: 17.2b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite108.0ms

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))
83.0ms	(+ (/ (- 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)

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

prune148.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.5b

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

rewrite353.0ms

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:

219.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ beta (+ (+ alpha beta) 2.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series228.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (37.0ms)

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

prune269.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.5b

localize16.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

95.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
139.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
145.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
143.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify117.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	333	1077
1	892	1029
2	4058	992
3	5001	980

prune351.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.9b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
14×	`log-prod`
12×	`distribute-lft-out`
8×	`log-div`
7×	`add-exp-log` `exp-sum` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`flip3--` `associate-/r*` `flip--`
4×	`exp-prod` `exp-diff` `frac-sub`
3×	`associate-/l*`
2×	`associate-/r/` `log-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 95

Calls

4 calls:

17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
169.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
168.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
57.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
122.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	462	1120
1	1490	1058
2	5001	1031

prune264.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

regimes117.0ms

Accuracy

77% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.6b

bsearch62.0ms

Steps

Iters	Range		Point
9	531.7447489915417	834758988592.4675	4012978693.971179

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	27
1	40	27

end0.0ms

sample905.0ms

Algorithm

intervals

Results

297.0ms	5858×	body	80	valid
160.0ms	891×	body	1280	valid
146.0ms	8000×	pre	80	true
95.0ms	687×	body	640	valid
40.0ms	376×	body	320	valid
15.0ms	188×	body	160	valid