Details

analyze2.0ms

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

sample43.0ms

Algorithm

intervals

Results

6.0ms	185×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	24×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	4×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5002	13

prune5.0ms

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: 16.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
16.7b	(+ (/ (- 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)

series19.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
11.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5370	1005

prune134.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

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: 16.1b

Counts

72 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
16.7b	(- (/ 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:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
25.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
15.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ beta (+ (+ alpha beta) 2.0))
10.0ms	(/ alpha (+ beta (+ alpha 2.0)))
11.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	6016	1670

prune195.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	126	7	133

Merged error: 2.6b

Counts

133 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
0.1b	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
0.1b	(* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
16.7b	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
41×	`times-frac`
39×	`unpow-prod-down` `cube-prod`
27×	`add-cube-cbrt`
24×	`associate-*r/` `difference-of-squares`
23×	`flip3-+` `flip-+`
18×	`associate-/l/` `distribute-lft-out`
16×	`frac-sub`
14×	`add-exp-log` `add-cbrt-cube`
12×	`frac-times` `associate-/r/`
11×	`sqr-pow`
8×	`flip3--` `flip--`
7×	`pow1`
6×	`associate-*l/` `add-log-exp`
5×	`distribute-lft-out--`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-r` `associate-l` `div-inv` `associate-/l*`
2×	`pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

9.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
22.0ms	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
7.0ms	(* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
39.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

series163.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
91.0ms	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
40.0ms	(* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
20.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5260	6031

prune858.0ms

Filtered

118 candidates to 185 candidates (-56.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	182	10	192

Merged error: 2.6b

Counts

192 → 10

localize20.0ms

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)))
16.7b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite29.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ alpha (+ beta 2.0)))
19.0ms	(cbrt (+ alpha (+ beta 2.0)))
17.0ms	(cbrt (+ alpha (+ beta 2.0)))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify29.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5240	838

prune156.0ms

Filtered

57 candidates to 71 candidates (-24.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	71	10	81

Merged error: 2.6b

Counts

81 → 10

regimes164.0ms

Accuracy

77.6% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 16.7b

bsearch21.0ms

Steps

Iters	Range		Point
8	4.436249952446616e+24	2.0996487308030442e+28	4.4939821187056533e+24

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	286	50
1	286	50

end0.0ms

sample1.0s

Algorithm

intervals

Results

174.0ms	5781×	body	80	valid
130.0ms	854×	body	1280	valid
96.0ms	804×	body	640	valid
33.0ms	360×	body	320	valid
12.0ms	201×	body	160	valid

Details

analyze2.0ms

sample43.0ms

simplify57.0ms

prune5.0ms

localize8.0ms

rewrite29.0ms

series19.0ms

simplify49.0ms

prune134.0ms

localize12.0ms

rewrite58.0ms

series39.0ms

simplify47.0ms

prune195.0ms

localize22.0ms

rewrite85.0ms

series163.0ms

simplify56.0ms

prune858.0ms

localize20.0ms

rewrite29.0ms

series64.0ms

simplify29.0ms

prune156.0ms

regimes164.0ms

bsearch21.0ms

simplify6.0ms

end0.0ms

sample1.0s

Profiling