Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	256×	pre	80	true
6.0ms	190×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	25×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	7×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (100.0%)

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: 15.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

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))
18.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series21.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
14.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune120.0ms

Filtered

71 candidates to 46 candidates (35.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 14.7b

Counts

72 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite61.0ms

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:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
29.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series35.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ alpha (+ (+ alpha beta) 2.0))
11.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (37.0ms)

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

prune192.0ms

Filtered

123 candidates to 84 candidates (31.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Merged error: 2.9b

Counts

136 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
2.4b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity`
131×	`times-frac`
89×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`pow1`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 200

Calls

4 calls:

32.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
28.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
17.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series59.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
10.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
20.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	825	2427
1	4052	2191
2	5002	2151

prune356.0ms

Filtered

212 candidates to 125 candidates (41.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	212	9	221

Merged error: 2.9b

Counts

221 → 9

localize21.0ms

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	(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
2.4b	(- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

364×	`*-un-lft-identity`
200×	`times-frac`
158×	`add-exp-log` `add-cbrt-cube`
144×	`distribute-lft-out`
129×	`pow1`
124×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
79×	`swap-sqr`
73×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
43×	`associate-r` `associate-l`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
20×	`pow-plus`
19×	`frac-times`
16×	`associate-/r/`
15×	`pow2`
13×	`associate-r/` `associate-l/`
9×	`unswap-sqr`
8×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
3×	`*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 351

Calls

4 calls:

25.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
28.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
38.0ms	(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
38.0ms	(- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
10.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
14.0ms	(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
24.0ms	(- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0)))

simplify127.0ms

Algorithm

egg-herbie

Counts

363 → 363

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	894	3946
1	4053	2836
2	5001	2727

prune629.0ms

Filtered

363 candidates to 141 candidates (61.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	362	1	363
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	363	9	372

Merged error: 2.9b

Counts

372 → 9

regimes281.0ms

Accuracy

97.9% (0.3b remaining)

Error of 3.3b against oracle of 3.0b and baseline of 15.7b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	26
1	40	26
2	42	26
3	42	26

end0.0ms

sample846.0ms

Algorithm

intervals

Results

200.0ms	5852×	body	80	valid
135.0ms	8000×	pre	80	true
133.0ms	826×	body	1280	valid
99.0ms	722×	body	640	valid
39.0ms	408×	body	320	valid
12.0ms	192×	body	160	valid

Details

sample38.0ms

simplify74.0ms

prune3.0ms

localize8.0ms

rewrite30.0ms

series21.0ms

simplify36.0ms

prune120.0ms

localize9.0ms

rewrite61.0ms

series35.0ms

simplify49.0ms

prune192.0ms

localize14.0ms

rewrite97.0ms

series59.0ms

simplify125.0ms

prune356.0ms

localize21.0ms

rewrite156.0ms

series58.0ms

simplify127.0ms

prune629.0ms

regimes281.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample846.0ms

Profiling