Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
3.0ms	27×	body	1280	valid
3.0ms	256×	pre	80	true
1.0ms	14×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	9×	body	160	valid

simplify74.0ms

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: 14.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite214.0ms

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:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
162.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series124.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune162.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
31×	`times-frac`
28×	`add-sqr-sqrt`
24×	`distribute-lft-out`
23×	`add-cube-cbrt`
10×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 89

Calls

3 calls:

37.0ms	(/ alpha (+ (+ alpha beta) 2.0))
37.0ms	(/ beta (+ (+ alpha beta) 2.0))
189.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series184.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
83.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify154.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	328	582
1	1072	553
2	4888	544
3	5001	544

prune234.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize13.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite252.0ms

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:

186.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
23.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
155.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
149.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
156.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify119.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (107.0ms)

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

prune371.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize16.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.1b	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
84×	`cbrt-prod`
60×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`distribute-lft-out`
25×	`log-pow`
24×	`exp-prod`
8×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
3×	`cbrt-div` `log-prod` `pow1/3`
1×	`rem-log-exp`

Counts

4 → 126

Calls

4 calls:

19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
20.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
83.0ms	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
157.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
153.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
158.0ms	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	277	1194
1	676	1135
2	2748	1095
3	5001	1079

prune476.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

regimes202.0ms

Accuracy

98.9% (0.1b remaining)

Error of 3.0b against oracle of 2.9b and baseline of 16.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	25
1	34	25

end0.0ms

sample644.0ms

Algorithm

intervals

Results

146.0ms	5812×	body	80	valid
111.0ms	836×	body	1280	valid
87.0ms	8000×	pre	80	true
75.0ms	742×	body	640	valid
27.0ms	378×	body	320	valid
12.0ms	232×	body	160	valid