Details

analyze3.0ms

Algorithm: search

sample27.0ms

Algorithm

intervals

Results

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

simplify80.0ms

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: 2.9b

Counts

2 → 1

localize15.0ms

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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite108.0ms

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:

11.0ms	(+ (+ (+ 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)))
35.0ms	(/ (/ (/ (+ (+ (+ 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)))

series62.0ms

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)))

simplify144.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.4s

Filtered

281 candidates to 477 candidates (-69.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	467	10	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	468	10	478

Merged error: 1.4b

Counts

478 → 10

localize13.0ms

Local error

Found 3 expressions with local error:

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)))

2.7b

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
827×	`*-un-lft-identity`
382×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
32×	`flip3-+` `flip-+`
31×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 511

Calls

3 calls:

22.0ms

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

35.0ms

(/ (/ (/ (+ (+ (+ 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)))

series60.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms

(/ (/ (+ (+ (+ 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 3.0)))

12.0ms

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

simplify149.0ms

Algorithm

egg-herbie

Counts

520 → 520

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1455	13746
1	5002	13200

prune1.0s

Filtered

268 candidates to 520 candidates (-94.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	518	2	520
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	520	10	530

Merged error: 1.4b

Counts

530 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ alpha (+ beta 3.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

4243×	`times-frac`
2956×	`*-un-lft-identity`
1613×	`add-sqr-sqrt` `add-cube-cbrt`
763×	`distribute-lft-out`
192×	`associate-/l*`
174×	`associate-/r/`
102×	`div-inv`
85×	`associate-/r*`
74×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1` `associate-/l/`
4×	`frac-2neg` `clear-num` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1515

Calls

4 calls:

19.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
25.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
67.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 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)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
20.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
29.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 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)))

simplify486.0ms

Algorithm

egg-herbie

Counts

1527 → 1527

Iterations

Useful iterations: 1 (75.0ms)

Iter	Nodes	Cost
0	4029	45774
1	5001	44391

prune5.2s

Filtered

708 candidates to 1527 candidates (-115.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1526	1	1527
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	1530	7	1537

Merged error: 0b

Counts

1537 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ 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)))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ 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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

1471×	`times-frac`
1040×	`*-un-lft-identity`
673×	`add-sqr-sqrt`
627×	`sqrt-prod`
590×	`add-cube-cbrt`
258×	`associate-r`
225×	`distribute-lft-out`
88×	`associate-/r/`
71×	`associate-/l*`
63×	`associate-l`
46×	`flip3-+` `flip-+`
44×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 761

Calls

4 calls:

255.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ 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)))
37.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ 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)))
22.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify253.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1953	24980
1	5001	24018

prune5.2s

Filtered

494 candidates to 773 candidates (-56.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	773	7	780

Merged error: 0b

Counts

780 → 7

regimes310.0ms

Accuracy

72.9% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.9b

bsearch43.0ms

Steps

Iters	Range		Point
8	2.106353878855238e+159	1.4854207050144666e+162	2.2685741156185878e+159

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	39	23

end0.0ms

analyze3.0ms

Algorithm: search

sample764.0ms

Algorithm

intervals

Results

498.0ms	8000×	body	80	valid
131.0ms	8000×	pre	80	true

Details

analyze3.0ms

sample27.0ms

simplify80.0ms

prune3.0ms

localize15.0ms

rewrite108.0ms

series62.0ms

simplify144.0ms

prune1.4s

localize13.0ms

rewrite109.0ms

series60.0ms

simplify149.0ms

prune1.0s

localize17.0ms

rewrite295.0ms

series84.0ms

simplify486.0ms

prune5.2s

localize15.0ms

rewrite397.0ms

series74.0ms

simplify253.0ms

prune5.2s

regimes310.0ms

bsearch43.0ms

simplify2.0ms

end0.0ms

analyze3.0ms

sample764.0ms

Profiling