Details

sample28.0ms

Algorithm

intervals

Results

5.0ms	182×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	28×	body	1280	valid
3.0ms	26×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	7×	body	160	valid

simplify72.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 17.6b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- 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))
17.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune142.0ms

Filtered

71 candidates to 46 candidates (64.8%)

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: 16.7b

Counts

72 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.6b	(- (/ 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:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series236.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (38.0ms)

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

prune250.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	9	123
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 3.7b

Counts

132 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.6b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite93.0ms

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:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
31.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
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))

series339.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ beta (+ (+ alpha beta) 2.0))
137.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
63.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
93.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify131.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (101.0ms)

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

prune370.0ms

Filtered

212 candidates to 125 candidates (59.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	212	10	222

Merged error: 3.7b

Counts

222 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.5b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

146×	`*-un-lft-identity`
119×	`add-sqr-sqrt` `times-frac`
81×	`sqrt-prod`
68×	`add-cube-cbrt`
42×	`distribute-lft-out`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`flip3-+` `cbrt-unprod` `flip-+` `div-inv`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 218

Calls

4 calls:

33.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
8.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
13.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series295.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
84.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
69.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify88.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	739	2243
1	3430	1926
2	5001	1771

prune336.0ms

Filtered

230 candidates to 115 candidates (50.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	226	4	230
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	230	10	240

Merged error: 3.7b

Counts

240 → 10

Details

sample28.0ms

simplify72.0ms

prune2.0ms

localize12.0ms

rewrite30.0ms

series110.0ms

simplify38.0ms

prune142.0ms

localize9.0ms

rewrite61.0ms

series236.0ms

simplify50.0ms

prune250.0ms

localize13.0ms

rewrite93.0ms

series339.0ms

simplify131.0ms

prune370.0ms

localize13.0ms

rewrite78.0ms

series295.0ms

simplify88.0ms

prune336.0ms

regimes239.0ms

bsearch3.0ms

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