Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample28.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune10.0ms

Filtered

1 candidates to 1 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: 5.9b

Counts

2 → 2

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))
5.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite111.0ms

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)
18.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
38.0ms	(/ (/ (/ (+ (+ (+ 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)))

series56.0ms

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))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify165.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5016	23485

prune1.5s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	472	7	479

Merged error: 1.7b

Counts

479 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.5b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
91×	`sqrt-prod`
82×	`times-frac`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt`
56×	`distribute-lft-out`
14×	`associate-/r*`
12×	`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 → 174

Calls

4 calls:

17.0ms	(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
15.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
16.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
9.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5035	4858

prune435.0ms

Filtered

106 candidates to 186 candidates (-75.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	186	7	193

Merged error: 1.7b

Counts

193 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
0.2b	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
5.5b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
5.5b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
64×	`times-frac`
60×	`sqrt-prod`
54×	`distribute-lft-out`
46×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
16×	`associate-/l*`
8×	`add-exp-log` `sqrt-div` `associate-/r*` `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`

Counts

4 → 154

Calls

4 calls:

15.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
12.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
6.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4991	3974
1	4991	3974

prune333.0ms

Filtered

98 candidates to 166 candidates (-69.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	166	7	173

Merged error: 1.7b

Counts

173 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)
0.1b	(/ (/ (cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
5.4b	(cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3))
5.5b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

2371×	`times-frac`
2324×	`*-un-lft-identity`
928×	`cbrt-prod`
887×	`add-sqr-sqrt` `add-cube-cbrt`
789×	`distribute-lft-out`
442×	`unpow-prod-down` `cube-prod`
194×	`associate-/l*`
82×	`associate-/r/`
42×	`flip3-+` `flip-+`
41×	`div-inv`
17×	`cube-mult` `unpow3` `sqr-pow`
14×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-div` `frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 1151

Calls

4 calls:

14.0ms	(pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)
67.0ms	(/ (/ (cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms	(cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3))
15.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)
29.0ms	(/ (/ (cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
12.0ms	(cbrt (pow (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) 3))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify467.0ms

Algorithm

egg-herbie

Counts

1163 → 1163

Iterations

Useful iterations: 0 (191.0ms)

Iter	Nodes	Cost
0	5024	63077

prune2.2s

Filtered

328 candidates to 1163 candidates (-254.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1162	1	1163
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	1163	7	1170

Merged error: 1.7b

Counts

1170 → 7

regimes122.0ms

Accuracy

53.1% (1.2b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 3.9b

bsearch23.0ms

Steps

Iters	Range		Point
4	9.391219314700689e+190	1.3297780489954926e+191	1.2687380306321451e+191

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	89
1	59	89

end0.0ms

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample739.0ms

Algorithm

intervals

Results

475.0ms	8000×	body	80	valid
130.0ms	8000×	pre	80	true

Details

analyze4.0ms

sample28.0ms

simplify112.0ms

prune10.0ms

localize12.0ms

rewrite111.0ms

series56.0ms

simplify165.0ms

prune1.5s

localize27.0ms

rewrite51.0ms

series104.0ms

simplify60.0ms

prune435.0ms

localize17.0ms

rewrite46.0ms

series105.0ms

simplify49.0ms

prune333.0ms

localize19.0ms

rewrite235.0ms

series84.0ms

simplify467.0ms

prune2.2s

regimes122.0ms

bsearch23.0ms

simplify1.0ms

end0.0ms

analyze3.0ms

sample739.0ms

Profiling