Details

sample30.0ms

Algorithm

intervals

Results

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

simplify81.0ms

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

prune3.0ms

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: 4.1b

Counts

2 → 1

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))
3.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite121.0ms

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)
19.0ms	(/ (/ (+ (+ (+ 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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ 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)))
23.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify142.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.4s

Filtered

281 candidates to 477 candidates (-69.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	471	7	478

Merged error: 0.8b

Counts

478 → 7

localize14.0ms

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)))

3.8b

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

rewrite123.0ms

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:

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 3.0)))

14.0ms

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

series62.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms

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

23.0ms

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

simplify149.0ms

Algorithm

egg-herbie

Counts

520 → 520

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1455	13746
1	5002	13200

prune1.1s

Filtered

268 candidates to 520 candidates (-94.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	518	2	520
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	520	7	527

Merged error: 0.8b

Counts

527 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
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) (+ (+ alpha beta) (* 2.0 1.0))))) (+ alpha (+ beta 3.0)))
3.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

4243×	`times-frac`
2956×	`*-un-lft-identity`
1613×	`add-sqr-sqrt` `add-cube-cbrt`
763×	`distribute-lft-out`
192×	`associate-/l*`
174×	`associate-/r/`
102×	`div-inv`
85×	`associate-/r*`
74×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1` `associate-/l/`
4×	`frac-2neg` `clear-num` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1515

Calls

4 calls:

25.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
27.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
69.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ alpha (+ beta 3.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
21.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
29.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 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)))

simplify477.0ms

Algorithm

egg-herbie

Counts

1527 → 1527

Iterations

Useful iterations: 1 (79.0ms)

Iter	Nodes	Cost
0	4029	45771
1	5001	44403

prune5.6s

Filtered

707 candidates to 1527 candidates (-116.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1525	2	1527
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	1527	7	1534

Merged error: 0b

Counts

1534 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.5b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.9b	(* (/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
3.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

1092×	`times-frac`
624×	`add-sqr-sqrt`
543×	`*-un-lft-identity`
351×	`add-cube-cbrt`
189×	`add-exp-log`
183×	`sqrt-prod`
174×	`cbrt-prod`
162×	`associate-l`
132×	`associate-r`
105×	`div-exp`
87×	`add-cbrt-cube`
86×	`distribute-lft-out`
65×	`unswap-sqr`
62×	`cbrt-undiv`
60×	`associate-/r/`
48×	`prod-exp`
33×	`flip3-+` `flip-+`
32×	`div-inv`
30×	`cbrt-unprod`
25×	`associate-/l*`
16×	`cbrt-div` `sqrt-div` `associate-/r*`
8×	`pow1`
7×	`rec-exp` `1-exp`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow-flip` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l/`
1×	`sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 675

Calls

4 calls:

25.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
8.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
317.0ms	(* (/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
31.0ms	(* (/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify240.0ms

Algorithm

egg-herbie

Counts

687 → 687

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2817	23940
1	5001	21123

prune5.4s

Filtered

419 candidates to 687 candidates (-64.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	687	0	687
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	687	7	694

Merged error: 0b

Counts

694 → 7

regimes115.0ms

Accuracy

71.8% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.8b

bsearch21.0ms

Steps

Iters	Range		Point
9	1.6748095093062562e+154	5.6060935474278676e+159	5.994544718051837e+157

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	39	23

end0.0ms

sample820.0ms

Algorithm

intervals

Results

468.0ms	8000×	body	80	valid
124.0ms	8000×	pre	80	true

Details

sample30.0ms

simplify81.0ms

prune3.0ms

localize12.0ms

rewrite121.0ms

series58.0ms

simplify142.0ms

prune1.4s

localize14.0ms

rewrite123.0ms

series62.0ms

simplify149.0ms

prune1.1s

localize15.0ms

rewrite328.0ms

series88.0ms

simplify477.0ms

prune5.6s

localize21.0ms

rewrite431.0ms

series106.0ms

simplify240.0ms

prune5.4s

regimes115.0ms

bsearch21.0ms

simplify1.0ms

end0.0ms

sample820.0ms

Profiling