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

sample32.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify141.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune8.0ms

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: 4.1b

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))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms

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:

8.0ms	(+ (+ (+ 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)))
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)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ 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)))
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)))

simplify195.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	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: 1.4b

Counts

479 → 7

localize13.0ms

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 3.0)))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
828×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
33×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 524

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ 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 3.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
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 3.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify171.0ms

Algorithm

egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5040	24742

prune1.4s

Filtered

285 candidates to 536 candidates (-88.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	534	2	536
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	536	7	543

Merged error: 1.4b

Counts

543 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
0.0b	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0)))
0.1b	(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0))))
3.9b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

845×	`*-un-lft-identity`
539×	`times-frac`
374×	`distribute-lft-out`
226×	`add-sqr-sqrt`
196×	`add-cube-cbrt`
136×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube` `associate-/l*`
32×	`associate-/r/`
24×	`div-exp`
18×	`associate-l`
17×	`flip3-+` `flip-+`
16×	`div-inv`
14×	`cbrt-undiv`
13×	`associate-/r*`
12×	`prod-exp`
9×	`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 → 453

Calls

4 calls:

6.0ms	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
22.0ms	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0)))
73.0ms	(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0))))
13.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
22.0ms	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0)))
22.0ms	(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify114.0ms

Algorithm

egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5223	14094

prune681.0ms

Filtered

201 candidates to 465 candidates (-131.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	465	0	465
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	465	7	472

Merged error: 1.4b

Counts

472 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

309×	`*-un-lft-identity`
204×	`sqrt-prod`
202×	`times-frac`
128×	`distribute-lft-out`
109×	`add-sqr-sqrt`
93×	`add-cube-cbrt`
70×	`associate-l`
50×	`associate-r`
47×	`add-exp-log` `add-cbrt-cube`
18×	`cbrt-undiv` `div-exp`
16×	`sqrt-div`
14×	`prod-exp` `associate-/r/` `cbrt-unprod`
12×	`flip3-+` `flip-+`
8×	`pow1` `associate-/r` `associate-/l`
5×	`frac-times` `unswap-sqr`
4×	`div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`sqrt-undiv` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 288

Calls

4 calls:

16.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
89.0ms	(* (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))) (/ (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))) (* (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
28.0ms	(* (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))) (/ (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))) (* (+ alpha (+ beta (* 1.0 2.0))) (sqrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify108.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4973	11377
1	4973	11377

prune732.0ms

Filtered

144 candidates to 300 candidates (-108.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	300	7	307

Merged error: 1.4b

Counts

307 → 7

regimes111.0ms

Accuracy

51.3% (1.2b remaining)

Error of 2.5b against oracle of 1.4b and baseline of 3.8b

bsearch12.0ms

Steps

Iters	Range		Point
6	9.788767425036225e+160	9.07647136578958e+161	5.016831569341494e+161

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	36
1	28	36

end0.0ms

sample741.0ms

Algorithm

intervals

Results

484.0ms	8000×	body	80	valid
126.0ms	8000×	pre	80	true

Details

analyze3.0ms

sample32.0ms

simplify141.0ms

prune8.0ms

localize12.0ms

rewrite116.0ms

series59.0ms

simplify195.0ms

prune1.5s

localize13.0ms

rewrite120.0ms

series58.0ms

simplify171.0ms

prune1.4s

localize17.0ms

rewrite147.0ms

series61.0ms

simplify114.0ms

prune681.0ms

localize20.0ms

rewrite136.0ms

series63.0ms

simplify108.0ms

prune732.0ms

regimes111.0ms

bsearch12.0ms

simplify1.0ms

end0.0ms

sample741.0ms

Profiling