Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	186×	body	80	valid
5.0ms	34×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

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: 16.7b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- 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)

series109.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- 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

prune144.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 16.0b

Counts

72 → 10

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))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite60.0ms

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:

30.0ms	(- (/ 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))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series235.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ beta (+ (+ 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

prune237.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	128	5	133

Merged error: 2.9b

Counts

133 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.1b	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
12.0ms	(/ 1 (+ (+ alpha beta) 2.0))
13.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
40.0ms	(/ 1 (+ (+ alpha beta) 2.0))
45.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	446	831
1	1808	750
2	5001	695

prune209.0ms

Filtered

149 candidates to 85 candidates (57.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	149	5	154

Merged error: 2.9b

Counts

154 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite18.0ms

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

series822.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(cbrt beta)
178.0ms	(cbrt beta)
180.0ms	(cbrt beta)
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (44.0ms)

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

prune136.0ms

Filtered

60 candidates to 50 candidates (83.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	60	5	65

Merged error: 2.9b

Counts

65 → 5

regimes78.0ms

Accuracy

71.3% (3.9b remaining)

Error of 6.9b against oracle of 3.0b and baseline of 16.6b

bsearch61.0ms

Steps

Iters	Range		Point
10	2656767.1297794953	1.6413741567260964e+21	13367189.758795647

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	26
1	40	26

end0.0ms

sample713.0ms

Algorithm

intervals

Results

184.0ms	5910×	body	80	valid
126.0ms	8000×	pre	80	true
123.0ms	836×	body	1280	valid
90.0ms	697×	body	640	valid
32.0ms	356×	body	320	valid
12.0ms	201×	body	160	valid

Details

sample31.0ms

simplify76.0ms

prune2.0ms

localize9.0ms

rewrite29.0ms

series109.0ms

simplify37.0ms

prune144.0ms

localize10.0ms

rewrite60.0ms

series235.0ms

simplify49.0ms

prune237.0ms

localize11.0ms

rewrite49.0ms

series209.0ms

simplify53.0ms

prune209.0ms

localize20.0ms

rewrite18.0ms

series822.0ms

simplify49.0ms

prune136.0ms

regimes78.0ms

bsearch61.0ms

simplify2.0ms

end0.0ms

sample713.0ms

Profiling