Details

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

sample27.0ms

Algorithm

intervals

Results

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

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune13.0ms

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: 2.1b

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))
1.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite104.0ms

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)
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
34.0ms	(/ (/ (/ (+ (+ (+ 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)))

series61.0ms

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)))
28.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify159.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5016	23485

prune1.3s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	469	8	477
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	471	8	479

Merged error: 0.5b

Counts

479 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
1.7b	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
1.9b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
1.9b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

192×	`*-un-lft-identity`
109×	`times-frac`
80×	`distribute-lft-out`
57×	`sqrt-prod`
55×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
39×	`associate-/l*`
18×	`flip3-+` `flip-+`
16×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-div`
9×	`associate-/r*`
8×	`frac-times`
7×	`associate-l`
6×	`pow1`
5×	`associate-r` `div-inv` `associate-/l/`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative`

Counts

4 → 207

Calls

4 calls:

17.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
25.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
14.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
22.0ms	(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
11.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify96.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4994	6744
1	4994	6744

prune759.0ms

Filtered

136 candidates to 219 candidates (-61.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	219	8	227

Merged error: 0.5b

Counts

227 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.3b	(/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.9b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite847.0ms

Algorithm

rewrite-expression-head

Rules

14723×	`times-frac`
11755×	`*-un-lft-identity`
5147×	`add-sqr-sqrt`
5145×	`add-cube-cbrt`
4414×	`sqrt-prod`
3518×	`distribute-lft-out`
823×	`associate-/l*`
239×	`associate-/r/`
216×	`sqrt-div`
127×	`div-inv`
115×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 4213

Calls

4 calls:

211.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms	(/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
6.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
70.0ms	(/ (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))))
10.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
244.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify1.6s

Algorithm

egg-herbie

Counts

4225 → 4225

Iterations

Useful iterations: 0 (176.0ms)

Iter	Nodes	Cost
0	5397	337955

prune16.9s

Filtered

1084 candidates to 4225 candidates (-289.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	4225	0	4225
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	4225	8	4233

Merged error: 0.5b

Counts

4233 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (cbrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))))
1.9b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
1.9b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
1.9b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

582×	`*-un-lft-identity`
249×	`distribute-lft-out`
238×	`times-frac`
208×	`cbrt-prod`
121×	`add-sqr-sqrt`
97×	`add-cube-cbrt`
75×	`swap-sqr`
29×	`associate-r` `associate-l`
15×	`associate-/l*`
14×	`associate-/r/`
12×	`add-exp-log` `associate-/r*`
11×	`pow1`
10×	`flip3-+` `add-cbrt-cube` `flip-+`
9×	`unswap-sqr`
7×	`div-inv`
6×	`pow1/3` `associate-/l/`
4×	`cbrt-div` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 298

Calls

4 calls:

39.0ms	(* (cbrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (cbrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cbrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (cbrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
18.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify102.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5076	9979

prune1.1s

Filtered

152 candidates to 310 candidates (-103.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	310	8	318

Merged error: 0.5b

Counts

318 → 8

regimes124.0ms

Accuracy

58.1% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.8b

bsearch44.0ms

Steps

Iters	Range		Point
8	4.3392801848996125e+192	5.061536497647835e+196	4.399215967806733e+192

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	70
1	37	70

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

sample744.0ms

Algorithm

intervals

Results

479.0ms	8000×	body	80	valid
132.0ms	8000×	pre	80	true

Details

analyze3.0ms

sample27.0ms

simplify116.0ms

prune13.0ms

localize12.0ms

rewrite104.0ms

series61.0ms

simplify159.0ms

prune1.3s

localize22.0ms

rewrite78.0ms

series61.0ms

simplify96.0ms

prune759.0ms

localize22.0ms

rewrite847.0ms

series352.0ms

simplify1.6s

prune16.9s

localize21.0ms

rewrite97.0ms

series82.0ms

simplify102.0ms

prune1.1s

regimes124.0ms

bsearch44.0ms

simplify1.0ms

end0.0ms

analyze3.0ms

sample744.0ms

Profiling