Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
5.0ms	28×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	7×	body	160	valid

simplify67.0ms

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

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.5b

Counts

2 → 1

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)

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)

series20.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
12.0ms	(+ (/ (- 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

prune122.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 13.8b

Counts

72 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

29.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series39.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5002	1268

prune236.0ms

Filtered

103 candidates to 149 candidates (-44.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	155	7	162

Merged error: 2.8b

Counts

162 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.5b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.7b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
64×	`times-frac`
50×	`log-prod`
37×	`add-cube-cbrt`
25×	`exp-sum`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
12×	`distribute-lft-out`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod`
3×	`div-inv` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `associate-/r/` `log-pow`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `clear-num` `flip--` `flip-+` `rem-exp-log`

Counts

4 → 126

Calls

4 calls:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
31.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
27.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series53.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
14.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
20.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	536	1689
1	1566	1612
2	5002	1560

prune256.0ms

Filtered

94 candidates to 138 candidates (-46.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	136	9	145

Merged error: 2.8b

Counts

145 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)) 3))
0.6b	(pow (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)) 3)
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.7b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
25×	`log-prod` `times-frac`
21×	`add-cube-cbrt`
14×	`cbrt-prod`
10×	`pow1` `distribute-lft-out--`
8×	`add-exp-log` `unpow-prod-down` `cube-prod` `difference-of-squares`
6×	`add-log-exp`
5×	`log-pow` `add-cbrt-cube`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `rem-log-exp` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `log-div` `flip3--` `pow-pow` `pow1/3` `diff-log` `div-exp` `pow-exp` `flip--` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 99

Calls

4 calls:

3.0ms	(cbrt (pow (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)) 3))
2.0ms	(pow (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)) 3)
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
31.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series100.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (pow (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)) 3))
47.0ms	(pow (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)) 3)
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
21.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	488	1647
1	1565	1557
2	5001	1507

prune188.0ms

Filtered

67 candidates to 111 candidates (-65.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Merged error: 2.8b

Counts

120 → 10

regimes306.0ms

Accuracy

99.3% (0.1b remaining)

Error of 3.1b against oracle of 3.0b and baseline of 15.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	30
1	43	30

end0.0ms

sample818.0ms

Algorithm

intervals

Results

201.0ms	5942×	body	80	valid
131.0ms	806×	body	1280	valid
127.0ms	8000×	pre	80	true
85.0ms	669×	body	640	valid
36.0ms	375×	body	320	valid
13.0ms	208×	body	160	valid

Details

sample33.0ms

simplify67.0ms

prune3.0ms

localize8.0ms

rewrite29.0ms

series20.0ms

simplify36.0ms

prune122.0ms

localize9.0ms

rewrite63.0ms

series39.0ms

simplify57.0ms

prune236.0ms

localize13.0ms

rewrite83.0ms

series53.0ms

simplify53.0ms

prune256.0ms

localize16.0ms

rewrite52.0ms

series100.0ms

simplify52.0ms

prune188.0ms

regimes306.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample818.0ms

Profiling