Details

sample150.0ms

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

6.0ms	186×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	26×	body	1280	valid
3.0ms	27×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	4×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

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: 16.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series21.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
13.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune114.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 15.9b

Counts

72 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series43.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune178.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	126	6	132

Merged error: 3.0b

Counts

132 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

376×	`*-un-lft-identity`
211×	`times-frac`
172×	`add-sqr-sqrt`
144×	`distribute-lft-out`
124×	`associate-*r/`
102×	`add-cube-cbrt`
85×	`flip3-+` `flip-+`
78×	`swap-sqr`
72×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
48×	`associate-*l/`
42×	`associate-r` `associate-l` `associate-/r/`
33×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
18×	`pow1` `unpow-prod-down` `cube-prod`
10×	`cbrt-undiv` `div-exp` `sqr-pow`
9×	`prod-exp` `cbrt-unprod` `div-inv`
8×	`unswap-sqr`
6×	`add-log-exp`
5×	`distribute-lft-out--`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`difference-cubes` `sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*`

Counts

4 → 374

Calls

4 calls:

24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
58.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
39.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series149.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
11.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
104.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
23.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify125.0ms

Algorithm

egg-herbie

Counts

386 → 386

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1906	8492
1	5002	8140

prune4.3s

Filtered

236 candidates to 386 candidates (-63.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	383	3	386
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	386	6	392

Merged error: 2.9b

Counts

392 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) 0) (+ (+ alpha beta) 2.0)))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
141×	`times-frac`
131×	`add-sqr-sqrt`
99×	`associate-*r/`
90×	`distribute-lft-out`
73×	`add-cube-cbrt`
68×	`flip3-+` `flip-+`
66×	`associate-/l/`
64×	`frac-sub`
53×	`frac-times`
48×	`frac-add`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
35×	`associate-*l/`
26×	`flip3--` `flip--`
24×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
21×	`associate-r` `associate-l`
20×	`associate-/r/`
12×	`pow1`
11×	`sqr-pow`
7×	`cbrt-undiv` `div-exp` `div-inv`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 309

Calls

4 calls:

10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
27.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
53.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) 0) (+ (+ alpha beta) 2.0)))
41.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series128.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
10.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
80.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) 0) (+ (+ alpha beta) 2.0)))
22.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1796	5986
1	5003	5650

prune2.2s

Filtered

200 candidates to 321 candidates (-60.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	314	7	321
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	316	11	327

Merged error: 2.9b

Counts

327 → 11

regimes224.0ms

Accuracy

72.4% (3.8b remaining)

Error of 6.8b against oracle of 3.0b and baseline of 16.6b

bsearch21.0ms

Steps

Iters	Range		Point
7	2.4972346845431213e+36	8.1277735345031055e+37	2.523362944402159e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	26
1	45	26
2	47	26
3	47	26

end0.0ms

sample959.0ms

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

195.0ms	5803×	body	80	valid
144.0ms	8000×	pre	80	true
138.0ms	856×	body	1280	valid
96.0ms	741×	body	640	valid
39.0ms	380×	body	320	valid
14.0ms	220×	body	160	valid

Details

sample150.0ms

simplify69.0ms

prune3.0ms

localize8.0ms

rewrite34.0ms

series21.0ms

simplify37.0ms

prune114.0ms

localize10.0ms

rewrite62.0ms

series43.0ms

simplify48.0ms

prune178.0ms

localize27.0ms

rewrite181.0ms

series149.0ms

simplify125.0ms

prune4.3s

localize27.0ms

rewrite154.0ms

series128.0ms

simplify99.0ms

prune2.2s

regimes224.0ms

bsearch21.0ms

simplify2.0ms

end0.0ms

sample959.0ms

Profiling