Details

sample196.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 98.831177%

Results

16.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify81.0ms

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: 3.8b

Counts

2 → 1

localize16.0ms

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) (* 2.0 1.0)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
584×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 463

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)))
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))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
25.0ms	(/ (/ (+ (+ (+ 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)))

simplify136.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune1.4s

Filtered

280 candidates to 475 candidates (-69.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	468	7	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	7	476

Merged error: 0.9b

Counts

476 → 7

localize18.0ms

Local error

Found 4 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))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.6b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite986.0ms

Algorithm

rewrite-expression-head

Rules

12636×	`times-frac`
7880×	`*-un-lft-identity`
4760×	`add-sqr-sqrt` `add-cube-cbrt`
3872×	`sqrt-prod`
1560×	`distribute-lft-out`
544×	`associate-/r/`
508×	`associate-/l*`
273×	`flip3-+` `flip-+`
272×	`div-inv`
34×	`add-exp-log` `add-cbrt-cube`
20×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/r*`
5×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4069

Calls

4 calls:

20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
163.0ms	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
43.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ (+ (+ (+ 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))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
24.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.6s

Algorithm

egg-herbie

Counts

4081 → 4081

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5001	188001

prune1.4min

Filtered

1845 candidates to 4081 candidates (-121.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	4080	1	4081
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	4081	7	4088

Merged error: 0.9b

Counts

4088 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`cbrt-prod` `cbrt-div`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`flip3-+` `flip-+`
9×	`add-exp-log`
8×	`associate-/l/`
7×	`times-frac` `associate-/r*`
5×	`add-cbrt-cube` `distribute-lft-out`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

27.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
9.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series82.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	413	1532
1	1296	1439
2	5001	1406

prune456.0ms

Filtered

81 candidates to 93 candidates (-14.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	93	7	100

Merged error: 0.9b

Counts

100 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.7b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`associate-/r/`
11×	`distribute-lft-out`
9×	`add-log-exp`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`associate-r/` `associate-l` `associate-l/` `associate-/r*` `div-inv`
3×	`associate-r` `prod-exp` `sum-log` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
15.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 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)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
7.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 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)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify120.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	765	2456
1	4241	2233
2	5001	2233

prune270.0ms

Filtered

112 candidates to 153 candidates (-36.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	153	7	160

Merged error: 0.9b

Counts

160 → 7

regimes122.0ms

Accuracy

47.9% (1.7b remaining)

Error of 3.0b against oracle of 1.3b and baseline of 4.5b

bsearch33.0ms

Steps

Iters	Range		Point
10	6.377268107478225e+156	3.445828635472764e+166	1.8714054624212292e+166

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 98.831177%

Results

498.0ms	8000×	body	80	valid
138.0ms	8000×	pre	80	true

Details

sample196.0ms

simplify81.0ms

prune3.0ms

localize16.0ms

rewrite112.0ms

series62.0ms

simplify136.0ms

prune1.4s

localize18.0ms

rewrite986.0ms

series83.0ms

simplify1.6s

prune1.4min

localize20.0ms

rewrite53.0ms

series82.0ms

simplify46.0ms

prune456.0ms

localize13.0ms

rewrite68.0ms

series47.0ms

simplify120.0ms

prune270.0ms

regimes122.0ms

bsearch33.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling