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

sample24.0ms

Algorithm

intervals

Results

6.0ms	200×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5002	13

prune6.0ms

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: 12.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite33.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- 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)

simplify48.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5370	1005

prune116.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 12.1b

Counts

72 → 9

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	(/ alpha (+ beta (+ alpha 2.0)))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.9b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite58.0ms

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:

26.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
14.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series40.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
10.0ms	(/ alpha (+ beta (+ alpha 2.0)))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6016	1670

prune196.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 3.3b

Counts

129 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
4.7b	(cbrt (/ beta (+ alpha (+ beta 2.0))))
4.7b	(cbrt (/ beta (+ alpha (+ beta 2.0))))
4.7b	(cbrt (/ beta (+ alpha (+ beta 2.0))))

rewrite36.0ms

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 → 104

Calls

4 calls:

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

series78.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
21.0ms	(cbrt (/ beta (+ alpha (+ beta 2.0))))
21.0ms	(cbrt (/ beta (+ alpha (+ beta 2.0))))
24.0ms	(cbrt (/ beta (+ alpha (+ beta 2.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5082	1711

prune305.0ms

Filtered

92 candidates to 116 candidates (-26.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Merged error: 3.3b

Counts

124 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
0.1b	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
1.9b	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

301×	`add-sqr-sqrt`
184×	`times-frac`
171×	`*-un-lft-identity`
120×	`difference-of-squares`
111×	`unpow-prod-down` `cube-prod`
71×	`add-cube-cbrt`
51×	`sqr-pow`
36×	`associate-/l*`
30×	`distribute-lft-out`
25×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*` `associate-/r/`
6×	`add-log-exp`
5×	`pow1` `difference-cubes`
4×	`flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`flip3--` `frac-2neg` `pow-exp` `clear-num` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `diff-log` `unpow3` `div-sub`

Counts

4 → 292

Calls

4 calls:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
47.0ms	(/ (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
9.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
38.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

series81.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ beta (+ (+ alpha beta) 2.0))
36.0ms	(/ (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
18.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
20.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

simplify132.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4950	11517
1	4950	11517

prune899.0ms

Filtered

149 candidates to 304 candidates (-104.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	304	8	312

Merged error: 3.3b

Counts

312 → 8

regimes147.0ms

Accuracy

75.9% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.4b

bsearch23.0ms

Steps

Iters	Range		Point
10	0.8597966171454865	12223138373.093277	133438067.44146341

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	358	88
1	358	88

end0.0ms

sample707.0ms

Algorithm

intervals

Results

183.0ms	5930×	body	80	valid
130.0ms	8000×	pre	80	true
128.0ms	815×	body	1280	valid
84.0ms	686×	body	640	valid
35.0ms	363×	body	320	valid
12.0ms	206×	body	160	valid

Details

analyze3.0ms

sample24.0ms

simplify55.0ms

prune6.0ms

localize8.0ms

rewrite33.0ms

series20.0ms

simplify48.0ms

prune116.0ms

localize11.0ms

rewrite58.0ms

series40.0ms

simplify48.0ms

prune196.0ms

localize16.0ms

rewrite36.0ms

series78.0ms

simplify39.0ms

prune305.0ms

localize20.0ms

rewrite118.0ms

series81.0ms

simplify132.0ms

prune899.0ms

regimes147.0ms

bsearch23.0ms

simplify8.0ms

end0.0ms

sample707.0ms

Profiling