Details

analyze4.0ms

Algorithm: search

sample27.0ms

Algorithm

intervals

Results

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

simplify82.0ms

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: 3.3b

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))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

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)))
37.0ms	(/ (/ (/ (+ (+ (+ 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)))
21.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify144.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.5s

Filtered

281 candidates to 477 candidates (-69.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	471	6	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	472	6	478

Merged error: 1.4b

Counts

478 → 6

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)))

3.1b

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

rewrite106.0ms

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:

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 3.0)))

13.0ms

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

series59.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms

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

21.0ms

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

18.0ms

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

simplify154.0ms

Algorithm

egg-herbie

Counts

520 → 520

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1455	13746
1	5002	13200

prune1.1s

Filtered

269 candidates to 520 candidates (-93.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	517	3	520
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	520	6	526

Merged error: 1.4b

Counts

526 → 6

localize14.0ms

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)))) (+ (+ (+ 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)))) (/ (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)))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite375.0ms

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:

38.0ms	(/ (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))
236.0ms	(* (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)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (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))
29.0ms	(* (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)))
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)))

simplify247.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1953	24980
1	5001	24018

prune5.3s

Filtered

494 candidates to 773 candidates (-56.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	773	6	779

Merged error: 1.4b

Counts

779 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
3.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
16×	`add-exp-log`
15×	`flip3-+` `flip-+`
13×	`*-un-lft-identity`
12×	`cbrt-prod` `sqrt-div` `add-cbrt-cube`
8×	`frac-times` `associate-/r/` `associate-/l/`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 79

Calls

4 calls:

30.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
6.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series98.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
14.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
18.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	623	1767
1	2249	1604
2	5002	1592

prune405.0ms

Filtered

77 candidates to 91 candidates (-18.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	91	6	97

Merged error: 1.4b

Counts

97 → 6

regimes106.0ms

Accuracy

60.6% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.9b

bsearch41.0ms

Steps

Iters	Range		Point
7	5.318184639772075e+170	1.1101049205334807e+173	4.624775698905151e+171

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	29
1	43	29

end0.0ms

analyze3.0ms

Algorithm: search

sample739.0ms

Algorithm

intervals

Results

481.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true

Details

analyze4.0ms

sample27.0ms

simplify82.0ms

prune3.0ms

localize12.0ms

rewrite112.0ms

series55.0ms

simplify144.0ms

prune1.5s

localize13.0ms

rewrite106.0ms

series59.0ms

simplify154.0ms

prune1.1s

localize14.0ms

rewrite375.0ms

series73.0ms

simplify247.0ms

prune5.3s

localize24.0ms

rewrite52.0ms

series98.0ms

simplify64.0ms

prune405.0ms

regimes106.0ms

bsearch41.0ms

simplify1.0ms

end0.0ms

analyze3.0ms

sample739.0ms

Profiling