Details

sample46.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

Filtered

1 candidates to 0 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: 3.9b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 463

Calls

4 calls:

10.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ 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))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ alpha beta) (* beta alpha))
136.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
154.0ms	(/ (/ (/ (+ (+ (+ 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))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify146.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune933.0ms

Filtered

475 candidates to 280 candidates (58.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	467	8	475
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	467	9	476

Merged error: 0.7b

Counts

476 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
17.4b	(sqrt (/ (/ (/ (+ (+ (+ 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)))
17.4b	(sqrt (/ (/ (/ (+ (+ (+ 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)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

1236×	`times-frac`
888×	`*-un-lft-identity`
508×	`add-sqr-sqrt`
492×	`sqrt-prod`
488×	`add-cube-cbrt`
200×	`distribute-lft-out`
72×	`associate-/r/`
38×	`flip3-+` `flip-+`
36×	`div-inv`
8×	`add-exp-log` `rem-sqrt-square` `add-cbrt-cube` `associate-/l*`
6×	`pow1` `associate-/r*`
4×	`associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 590

Calls

4 calls:

15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
54.0ms	(sqrt (/ (/ (/ (+ (+ (+ 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)))
52.0ms	(sqrt (/ (/ (/ (+ (+ (+ 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)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
71.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
291.0ms	(sqrt (/ (/ (/ (+ (+ (+ 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)))
291.0ms	(sqrt (/ (/ (/ (+ (+ (+ 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)))

simplify217.0ms

Algorithm

egg-herbie

Counts

602 → 602

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1580	20724
1	5001	20206

prune1.5s

Filtered

602 candidates to 320 candidates (53.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	602	0	602
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	602	9	611

Merged error: 0.7b

Counts

611 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

17.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
16.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series418.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
107.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	507	2619
1	1928	2448
2	5001	2394

prune412.0ms

Filtered

171 candidates to 99 candidates (57.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	171	9	180

Merged error: 0.7b

Counts

180 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
12.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series194.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	124	600
1	398	568
2	1855	560
3	5002	560

prune289.0ms

Filtered

76 candidates to 60 candidates (78.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	76	9	85

Merged error: 0.7b

Counts

85 → 9

regimes124.0ms

Accuracy

90.5% (0.2b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 3.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	34
1	25	34

end0.0ms

sample633.0ms

Algorithm

intervals

Results

358.0ms	8000×	body	80	valid
128.0ms	8000×	pre	80	true