Details

sample27.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 3.8b

Counts

2 → 1

localize12.0ms

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:

6.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms	(/ (/ (/ (+ (+ (+ 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))
18.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
277.0ms	(/ (/ (+ (+ (+ 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))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify149.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune897.0ms

Filtered

475 candidates to 280 candidates (58.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	469	6	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	470	6	476

Merged error: 1.5b

Counts

476 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.1b	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

3618×	`times-frac`
2167×	`*-un-lft-identity`
1425×	`add-sqr-sqrt` `add-cube-cbrt`
371×	`distribute-lft-out`
248×	`associate-/l*`
158×	`associate-/r/`
89×	`div-inv`
70×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/r*`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1337

Calls

4 calls:

28.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
67.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series482.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
75.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
160.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
96.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify444.0ms

Algorithm

egg-herbie

Counts

1349 → 1349

Iterations

Useful iterations: 1 (70.0ms)

Iter	Nodes	Cost
0	3844	42670
1	5001	41449

prune2.3s

Filtered

1349 candidates to 696 candidates (51.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1347	2	1349
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	1349	6	1355

Merged error: 0.0b

Counts

1355 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.5b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.4b	(/ (/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
2.5b	(/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

5994×	`times-frac`
3630×	`*-un-lft-identity`
2348×	`add-sqr-sqrt` `add-cube-cbrt`
711×	`sqrt-prod`
641×	`distribute-lft-out`
395×	`associate-/l*`
151×	`associate-/r/`
85×	`div-inv`
67×	`flip3-+` `flip-+`
57×	`add-exp-log`
39×	`div-exp`
31×	`add-cbrt-cube`
18×	`cbrt-undiv`
17×	`associate-/r*`
6×	`pow1`
5×	`rec-exp` `1-exp`
4×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/` `add-log-exp`
3×	`pow-flip`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 1987

Calls

4 calls:

90.0ms	(/ (/ (/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
8.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
39.0ms	(/ (/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series675.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ (/ (/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
71.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
206.0ms	(/ (/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
179.0ms	(/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify678.0ms

Algorithm

egg-herbie

Counts

1999 → 1999

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4978	68361
1	5001	68361

prune4.9s

Filtered

1999 candidates to 1139 candidates (57.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1999	0	1999
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	1999	6	2005

Merged error: 0.0b

Counts

2005 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.6b	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite723.0ms

Algorithm

rewrite-expression-head

Rules

3553×	`times-frac`
2088×	`*-un-lft-identity`
1654×	`add-sqr-sqrt`
1436×	`add-cube-cbrt`
1370×	`sqrt-prod`
615×	`associate-r`
326×	`distribute-lft-out`
126×	`associate-/r/`
87×	`associate-/l*`
65×	`flip3-+` `flip-+`
63×	`div-inv`
55×	`associate-l`
45×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
22×	`cbrt-undiv` `div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-/r*`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 1497

Calls

4 calls:

44.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
466.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series630.0ms

Counts

4 → 12

Calls

4 calls:

386.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
147.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
44.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify514.0ms

Algorithm

egg-herbie

Counts

1509 → 1509

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	4302	53952
1	5001	52369

prune2.6s

Filtered

1509 candidates to 628 candidates (41.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1509	0	1509
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1509	6	1515

Merged error: 0.0b

Counts

1515 → 6

regimes65.0ms

Accuracy

72.1% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.9b

bsearch56.0ms

Steps

Iters	Range		Point
7	4.0917562849863095e+159	2.5534508082457815e+161	3.298192609819446e+160

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	34
1	39	34

end0.0ms

sample622.0ms

Algorithm

intervals

Results

348.0ms	8000×	body	80	valid
129.0ms	8000×	pre	80	true