Details

sample28.0ms

Algorithm

intervals

Results

5.0ms	179×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	29×	body	1280	valid
3.0ms	27×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	7×	body	160	valid

simplify75.0ms

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

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: 18.0b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- 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)

series112.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
65.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune152.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 17.2b

Counts

72 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

34.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series244.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5001	1268

prune296.0ms

Filtered

149 candidates to 103 candidates (69.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	140	9	149
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	150	11	161

Merged error: 3.5b

Counts

161 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.9b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

273×	`*-un-lft-identity`
153×	`times-frac`
139×	`add-sqr-sqrt`
102×	`distribute-lft-out`
81×	`add-cube-cbrt`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
24×	`difference-of-squares`
21×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
14×	`associate-/r/`
12×	`pow1`
11×	`sqr-pow`
7×	`flip3-+` `flip-+` `div-inv`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out--`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 250

Calls

4 calls:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
42.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series306.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ beta (+ (+ alpha beta) 2.0))
75.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
67.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
117.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	925	2341
1	5001	2046

prune529.0ms

Filtered

262 candidates to 131 candidates (50.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	261	12	273

Merged error: 3.5b

Counts

273 → 12

localize20.0ms

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)))
1.9b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
1.9b	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

255×	`*-un-lft-identity`
177×	`add-sqr-sqrt`
146×	`times-frac`
90×	`distribute-lft-out`
73×	`add-cube-cbrt`
57×	`unpow-prod-down` `cube-prod`
48×	`difference-of-squares`
39×	`swap-sqr`
34×	`log-pow`
33×	`exp-prod`
21×	`associate-r` `associate-l` `sqr-pow`
19×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
12×	`associate-/r/`
10×	`distribute-lft-out--`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`cbrt-undiv` `log-prod` `div-exp`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg` `exp-sum` `pow-exp` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `log-div` `flip3--` `pow-pow` `pow-plus` `exp-diff` `diff-log` `unpow3` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 261

Calls

4 calls:

10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
40.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
44.0ms	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
66.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
110.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
120.0ms	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

simplify170.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	915	2519
1	4923	2207
2	5001	2207

prune592.0ms

Filtered

273 candidates to 133 candidates (48.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	273	12	285

Merged error: 3.5b

Counts

285 → 12

regimes133.0ms

Accuracy

73.8% (3.3b remaining)

Error of 6.2b against oracle of 2.9b and baseline of 15.4b

bsearch57.0ms

Steps

Iters	Range		Point
8	1.0040126536157294e+24	8.32596087152137e+26	5.911479864986242e+26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	42
1	51	42

end0.0ms

sample700.0ms

Algorithm

intervals

Results

180.0ms	5886×	body	80	valid
129.0ms	839×	body	1280	valid
122.0ms	8000×	pre	80	true
79.0ms	671×	body	640	valid
33.0ms	388×	body	320	valid
13.0ms	216×	body	160	valid

Details

sample28.0ms

simplify75.0ms

prune2.0ms

localize12.0ms

rewrite30.0ms

series112.0ms

simplify36.0ms

prune152.0ms

localize9.0ms

rewrite68.0ms

series244.0ms

simplify63.0ms

prune296.0ms

localize17.0ms

rewrite104.0ms

series306.0ms

simplify53.0ms

prune529.0ms

localize20.0ms

rewrite135.0ms

series367.0ms

simplify170.0ms

prune592.0ms

regimes133.0ms

bsearch57.0ms

simplify2.0ms

end0.0ms

sample700.0ms

Profiling