Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample25.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
4.0ms	30×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	23×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5002	13

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite28.0ms

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))
16.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series20.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5370	1005

prune117.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 16.1b

Counts

72 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
1.5b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite55.0ms

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`
1×	`associate--r+` `associate--r-`

Counts

4 → 108

Calls

4 calls:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series35.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6016	1670

prune199.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Merged error: 4.5b

Counts

131 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ alpha (+ beta 2.0)))
0.0b	(/ alpha (+ alpha (+ beta 2.0)))
0.1b	(* (/ alpha (+ alpha (+ beta 2.0))) (/ alpha (+ alpha (+ beta 2.0))))
1.5b	(- (* (/ alpha (+ alpha (+ beta 2.0))) (/ alpha (+ alpha (+ beta 2.0)))) (* 1.0 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

244×	`*-un-lft-identity`
130×	`times-frac`
96×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`pow1`
10×	`associate-/r*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 195

Calls

4 calls:

7.0ms	(/ alpha (+ alpha (+ beta 2.0)))
7.0ms	(/ alpha (+ alpha (+ beta 2.0)))
21.0ms	(* (/ alpha (+ alpha (+ beta 2.0))) (/ alpha (+ alpha (+ beta 2.0))))
15.0ms	(- (* (/ alpha (+ alpha (+ beta 2.0))) (/ alpha (+ alpha (+ beta 2.0)))) (* 1.0 1.0))

series42.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ alpha (+ alpha (+ beta 2.0)))
6.0ms	(/ alpha (+ alpha (+ beta 2.0)))
10.0ms	(* (/ alpha (+ alpha (+ beta 2.0))) (/ alpha (+ alpha (+ beta 2.0))))
19.0ms	(- (* (/ alpha (+ alpha (+ beta 2.0))) (/ alpha (+ alpha (+ beta 2.0)))) (* 1.0 1.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4993	2831
1	4993	2831

prune320.0ms

Filtered

118 candidates to 207 candidates (-75.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Merged error: 4.5b

Counts

218 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ alpha (+ beta 2.0)))
0.7b	(cbrt (+ alpha (+ beta 2.0)))
0.7b	(cbrt (+ alpha (+ beta 2.0)))
1.5b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
14.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series61.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ alpha (+ beta 2.0)))
17.0ms	(cbrt (+ alpha (+ beta 2.0)))
17.0ms	(cbrt (+ alpha (+ beta 2.0)))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify30.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5240	838

prune155.0ms

Filtered

57 candidates to 71 candidates (-24.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	71	9	80

Merged error: 4.5b

Counts

80 → 9

regimes142.0ms

Accuracy

69% (3.9b remaining)

Error of 7.2b against oracle of 3.3b and baseline of 15.9b

bsearch14.0ms

Steps

Iters	Range		Point
6	9.428160642650705e+50	6.932571427764177e+51	9.936431395575482e+50

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	345	50
1	345	50

end0.0ms

sample705.0ms

Algorithm

intervals

Results

180.0ms	5808×	body	80	valid
124.0ms	823×	body	1280	valid
124.0ms	8000×	pre	80	true
87.0ms	733×	body	640	valid
40.0ms	402×	body	320	valid
16.0ms	234×	body	160	valid

Details

analyze3.0ms

sample25.0ms

simplify54.0ms

prune9.0ms

localize8.0ms

rewrite28.0ms

series20.0ms

simplify47.0ms

prune117.0ms

localize11.0ms

rewrite55.0ms

series35.0ms

simplify44.0ms

prune199.0ms

localize19.0ms

rewrite60.0ms

series42.0ms

simplify72.0ms

prune320.0ms

localize17.0ms

rewrite30.0ms

series61.0ms

simplify30.0ms

prune155.0ms

regimes142.0ms

bsearch14.0ms

simplify8.0ms

end0.0ms

sample705.0ms

Profiling