Details

sample31.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 0%

Results

16.0ms	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

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: 4.4b

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))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite114.0ms

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ 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)))
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))
11.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify143.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.3s

Filtered

281 candidates to 477 candidates (-69.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	468	9	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	9	478

Merged error: 1.9b

Counts

478 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
4.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt` `sqrt-prod`
38×	`add-cube-cbrt`
14×	`associate-/l*`
10×	`distribute-lft-out`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
6×	`pow1` `flip3-+` `associate-/r*` `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`

Counts

4 → 126

Calls

4 calls:

13.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series105.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
45.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	372	1870
1	1362	1788
2	5002	1762

prune300.0ms

Filtered

98 candidates to 138 candidates (-40.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	138	9	147

Merged error: 1.9b

Counts

147 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.3b	(* (/ (+ (+ (+ 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)))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

248×	`times-frac`
202×	`*-un-lft-identity`
152×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
66×	`associate-r`
54×	`add-exp-log`
38×	`distribute-lft-out`
34×	`add-cbrt-cube`
28×	`associate-/r/`
26×	`div-exp`
22×	`associate-/l*`
18×	`associate-l`
15×	`flip3-+` `flip-+`
14×	`cbrt-undiv` `div-inv`
10×	`prod-exp` `associate-/r*`
8×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 286

Calls

4 calls:

6.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
53.0ms	(* (/ (+ (+ (+ 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)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
10.0ms	(/ (/ 1 (+ (+ 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))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
11.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1120	5097
1	5001	4696

prune562.0ms

Filtered

185 candidates to 298 candidates (-61.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	298	9	307

Merged error: 1.9b

Counts

307 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 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))))
1.1b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

1422×	`times-frac`
1040×	`*-un-lft-identity`
604×	`add-sqr-sqrt` `add-cube-cbrt`
255×	`sqrt-prod`
218×	`distribute-lft-out`
133×	`associate-/l*`
56×	`associate-/r/`
42×	`sqrt-div`
29×	`flip3-+` `flip-+`
28×	`div-inv`
24×	`add-exp-log`
22×	`add-cbrt-cube`
19×	`associate-/r*`
12×	`div-exp`
11×	`cbrt-undiv`
6×	`pow1`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
3×	`pow-flip`
1×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`

Counts

4 → 740

Calls

4 calls:

45.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 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))))
25.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
35.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify224.0ms

Algorithm

egg-herbie

Counts

752 → 752

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2057	21889
1	5001	21450

prune2.7s

Filtered

394 candidates to 752 candidates (-90.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	751	1	752
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	752	9	761

Merged error: 1.9b

Counts

761 → 9

regimes173.0ms

Accuracy

50.6% (1.3b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.7b

bsearch41.0ms

Steps

Iters	Range		Point
8	5.003742343121288e+212	5.507200203762071e+216	5.447914656172989e+212

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	50
1	53	50

end0.0ms

sample794.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.823218%

Space saved by search: 43.823218%

Guaranteed chance to sample good point: 0%

Results

521.0ms	8000×	body	80	valid
134.0ms	8000×	pre	80	true

Details

sample31.0ms

simplify79.0ms

prune3.0ms

localize12.0ms

rewrite114.0ms

series55.0ms

simplify143.0ms

prune1.3s

localize13.0ms

rewrite46.0ms

series105.0ms

simplify50.0ms

prune300.0ms

localize13.0ms

rewrite102.0ms

series51.0ms

simplify69.0ms

prune562.0ms

localize16.0ms

rewrite153.0ms

series102.0ms

simplify224.0ms

prune2.7s

regimes173.0ms

bsearch41.0ms

simplify2.0ms

end0.0ms

sample794.0ms

Profiling