Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample27.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune9.0ms

Filtered

1 candidates to 1 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: 1.6b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

7.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
18.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify170.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5016	23485

prune1.5s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	472	7	479

Merged error: 0.5b

Counts

479 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))

1.5b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
827×	`*-un-lft-identity`
382×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
32×	`flip3-+` `flip-+`
31×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 511

Calls

3 calls:

18.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

36.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))

13.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series56.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

22.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))

13.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify222.0ms

Algorithm

egg-herbie

Counts

520 → 520

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	5002	23836

prune1.1s

Filtered

274 candidates to 520 candidates (-89.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	520	0	520
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	520	7	527

Merged error: 0.5b

Counts

527 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
1.1b	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
1.5b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
1.5b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

192×	`*-un-lft-identity`
109×	`times-frac`
80×	`distribute-lft-out`
57×	`sqrt-prod`
55×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
39×	`associate-/l*`
18×	`flip3-+` `flip-+`
16×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-div`
9×	`associate-/r*`
8×	`frac-times`
7×	`associate-l`
6×	`pow1`
5×	`associate-r` `div-inv` `associate-/l/`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative`

Counts

4 → 207

Calls

4 calls:

13.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
27.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
26.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify92.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4994	6744
1	4994	6744

prune685.0ms

Filtered

136 candidates to 219 candidates (-61.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	219	7	226

Merged error: 0.5b

Counts

226 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.8b	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.4b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

16774×	`times-frac`
13167×	`*-un-lft-identity`
6144×	`add-sqr-sqrt` `add-cube-cbrt`
4907×	`sqrt-prod`
3939×	`distribute-lft-out`
1060×	`associate-/l*`
298×	`associate-/r/`
284×	`sqrt-div`
150×	`flip3-+` `flip-+`
149×	`div-inv`
34×	`add-exp-log` `add-cbrt-cube`
20×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 5238

Calls

4 calls:

70.0ms	(/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
195.0ms	(/ (/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
28.0ms	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms	(/ (/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
24.0ms	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0)))))

simplify1.9s

Algorithm

egg-herbie

Counts

5250 → 5250

Iterations

Useful iterations: 0 (213.0ms)

Iter	Nodes	Cost
0	5586	376911

prune46.5s

Filtered

1517 candidates to 5250 candidates (-246.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	5249	1	5250
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	5250	7	5257

Merged error: 0.5b

Counts

5257 → 7

regimes115.0ms

Accuracy

0% (2.5b remaining)

Error of 3.6b against oracle of 1.1b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	31
1	24	31

end0.0ms

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample746.0ms

Algorithm

intervals

Results

483.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true

Details

analyze4.0ms

sample27.0ms

simplify112.0ms

prune9.0ms

localize12.0ms

rewrite110.0ms

series62.0ms

simplify170.0ms

prune1.5s

localize13.0ms

rewrite110.0ms

series56.0ms

simplify222.0ms

prune1.1s

localize19.0ms

rewrite74.0ms

series66.0ms

simplify92.0ms

prune685.0ms

localize19.0ms

rewrite1.3s

series100.0ms

simplify1.9s

prune46.5s

regimes115.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze3.0ms

sample746.0ms

Profiling