Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	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

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 6.4b

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))
6.0b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

29629×	`*-un-lft-identity`
17765×	`distribute-lft-out`
11948×	`times-frac`
4330×	`associate-l`
2249×	`add-sqr-sqrt` `add-cube-cbrt`
588×	`associate-/l*`
168×	`associate-/r/`
138×	`associate-/l/`
88×	`flip3-+` `flip-+`
84×	`div-inv`
43×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
6×	`frac-2neg` `clear-num`
4×	`pow1`
3×	`sum-log`
2×	`+-commutative` `associate-+l+`

Counts

4 → 4722

Calls

4 calls:

10.0ms	(+ (+ alpha beta) (* beta alpha))
56.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
201.0ms	(/ (/ (/ (+ (+ (+ 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))
25.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ alpha beta) (* beta alpha))
147.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
160.0ms	(/ (/ (/ (+ (+ (+ 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))
89.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.2s

Algorithm

egg-herbie

Counts

4734 → 4734

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	1596	115829
1	5001	114691

prune931.0ms

Filtered

4734 candidates to 310 candidates (93.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	4727	7	4734
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	4727	8	4735

Merged error: 2.1b

Counts

4735 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
6.0b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

5817×	`*-un-lft-identity`
3435×	`distribute-lft-out`
1717×	`times-frac`
1420×	`associate-l`
723×	`add-sqr-sqrt`
553×	`add-cube-cbrt`
520×	`frac-times`
512×	`associate-/r*`
463×	`associate-/l*`
354×	`associate-/l/`
270×	`associate-r`
75×	`clear-num`
73×	`frac-2neg`
64×	`add-exp-log`
60×	`unswap-sqr`
52×	`flip3-+` `flip-+`
46×	`associate-/r/`
40×	`associate-*l/`
38×	`add-cbrt-cube`
28×	`div-exp`
26×	`associate-*r/`
23×	`div-inv`
16×	`prod-exp`
15×	`cbrt-undiv`
10×	`*-commutative`
8×	`cbrt-unprod`
7×	`pow1`
6×	`un-div-inv`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 1778

Calls

4 calls:

11.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
78.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
136.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
28.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
161.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
87.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify395.0ms

Algorithm

egg-herbie

Counts

1790 → 1790

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	2090	35745
1	5001	34706

prune1.0s

Filtered

1790 candidates to 371 candidates (79.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1789	1	1790
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	1790	8	1798

Merged error: 2.1b

Counts

1798 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

5257×	`*-un-lft-identity`
2870×	`distribute-lft-out`
2749×	`sqrt-prod`
2480×	`times-frac`
765×	`add-sqr-sqrt`
763×	`add-cube-cbrt`
750×	`associate-l`
138×	`associate-/l*`
34×	`sqrt-div`
30×	`associate-/r*` `associate-/l/`
26×	`associate-/r/`
17×	`flip3-+` `flip-+`
13×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`sqrt-undiv` `frac-2neg` `clear-num`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 1517

Calls

4 calls:

91.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
27.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
13.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series446.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
121.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify393.0ms

Algorithm

egg-herbie

Counts

1529 → 1529

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1055	33536
1	4066	30682
2	5001	30655

prune726.0ms

Filtered

1529 candidates to 187 candidates (87.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1529	0	1529
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	1529	8	1537

Merged error: 2.1b

Counts

1537 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* (cbrt 1) (cbrt 1)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (* (cbrt 1) (cbrt 1)) (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))))
0.6b	(/ (/ (cbrt 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
6.0b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite10.2s

Algorithm

rewrite-expression-head

Rules

172449×	`*-un-lft-identity`
95788×	`distribute-lft-out`
68673×	`times-frac`
67635×	`cbrt-prod`
46774×	`add-sqr-sqrt`
34351×	`associate-l`
33386×	`associate-r`
24144×	`swap-sqr`
19431×	`sqrt-prod`
17703×	`add-cube-cbrt`
15836×	`unswap-sqr`
1609×	`associate-/l*`
1583×	`*-commutative`
1081×	`associate-/l/`
904×	`frac-times`
642×	`associate-/r*`
330×	`associate-/r/`
297×	`add-cbrt-cube`
214×	`flip3-+` `flip-+`
172×	`sqrt-div`
162×	`div-inv`
161×	`cbrt-undiv`
156×	`cbrt-unprod`
81×	`add-exp-log`
73×	`clear-num`
72×	`frac-2neg`
47×	`associate-*r/`
34×	`div-exp`
24×	`prod-exp`
22×	`associate-*l/`
14×	`cbrt-div`
4×	`pow1` `add-log-exp`
3×	`un-div-inv`

Counts

4 → 35662

Calls

4 calls:

27.0ms	(/ (* (cbrt 1) (cbrt 1)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.5s	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (* (cbrt 1) (cbrt 1)) (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))))
53.0ms	(/ (/ (cbrt 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
25.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series881.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (* (cbrt 1) (cbrt 1)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
501.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (* (cbrt 1) (cbrt 1)) (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))))
222.0ms	(/ (/ (cbrt 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
85.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify14.9s

Algorithm

egg-herbie

Counts

35674 → 35674

Iterations

Useful iterations: 0 (237.0ms)

Iter	Nodes	Cost
0	6505	1583597

prune31.4s

Filtered

35674 candidates to 5380 candidates (84.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	35673	1	35674
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	35673	9	35682

Merged error: 2.1b

Counts

35682 → 9

regimes162.0ms

Accuracy

89.6% (0.3b 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	31	35
1	31	35

end0.0ms

sample554.0ms

Algorithm

intervals

Results

312.0ms	8000×	body	80	valid
99.0ms	8000×	pre	80	true