Details

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

sample27.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify115.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

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: 3.3b

Counts

2 → 2

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) (* 2.0 1.0)) 1.0))

3.1b

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

20.0ms

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

39.0ms

(/ (/ (/ (+ (+ (+ 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))

14.0ms

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

series54.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms

(/ (/ (+ (+ (+ 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)))

simplify172.0ms

Algorithm

egg-herbie

Counts

459 → 459

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5522	23282

prune1.4s

Filtered

275 candidates to 459 candidates (-66.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	452	7	459
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	454	7	461

Merged error: 0.7b

Counts

461 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
0.0b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.2b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0)))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
80×	`times-frac`
54×	`add-exp-log`
51×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
18×	`associate-r` `associate-/r/` `distribute-lft-out`
14×	`cbrt-undiv`
13×	`flip3-+` `flip-+` `associate-/l*`
12×	`prod-exp`
11×	`associate-/r*`
9×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 188

Calls

4 calls:

6.0ms	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
24.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
27.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
17.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0)))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
20.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
12.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ alpha (+ beta (* 1.0 2.0)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4977	5617
1	4977	5617

prune376.0ms

Filtered

133 candidates to 200 candidates (-50.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	200	7	207

Merged error: 0.7b

Counts

207 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
2.5b	(/ (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))))))
3.1b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
3.1b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite80.0ms

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
21.0ms	(/ (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))))))
11.0ms	(/ (+ 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))))

simplify68.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5369	6744

prune762.0ms

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: 0.7b

Counts

226 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ alpha (+ beta (* 1.0 2.0))))
0.8b	(cbrt (+ alpha (+ beta (* 1.0 2.0))))
3.1b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
3.1b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `sqrt-prod`
8×	`cbrt-prod` `add-cube-cbrt` `distribute-lft-out`
6×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 62

Calls

4 calls:

4.0ms	(cbrt (+ alpha (+ beta (* 1.0 2.0))))
4.0ms	(cbrt (+ alpha (+ beta (* 1.0 2.0))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
8.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (+ alpha (+ beta (* 1.0 2.0))))
17.0ms	(cbrt (+ alpha (+ beta (* 1.0 2.0))))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify72.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4871	1030
1	4871	1030

prune219.0ms

Filtered

56 candidates to 74 candidates (-32.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	74	7	81

Merged error: 0.7b

Counts

81 → 7

regimes107.0ms

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	29	37
1	29	37

end0.0ms

sample771.0ms

Algorithm

intervals

Results

503.0ms	8000×	body	80	valid
133.0ms	8000×	pre	80	true

Details

analyze3.0ms

sample27.0ms

simplify115.0ms

prune9.0ms

localize13.0ms

rewrite109.0ms

series54.0ms

simplify172.0ms

prune1.4s

localize19.0ms

rewrite81.0ms

series59.0ms

simplify82.0ms

prune376.0ms

localize24.0ms

rewrite80.0ms

series61.0ms

simplify68.0ms

prune762.0ms

localize27.0ms

rewrite24.0ms

series54.0ms

simplify72.0ms

prune219.0ms

regimes107.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample771.0ms

Profiling