Details

sample22.0ms

Algorithm

intervals

Results

5.0ms	194×	body	80	valid
4.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	20×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify82.0ms

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	184	6
6	250	6
7	287	6
8	349	6
9	437	6
10	574	6
11	654	6
12	712	6
13	785	6
14	1075	6
15	1150	6
16	1193	6
17	1213	6
18	1221	6
19	1221	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: 14.7b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
24.0ms	(+ (/ (- 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)

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	329	555
1	1066	529
2	5002	525

prune169.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	12	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Merged error: 14.1b

Counts

107 → 12

localize8.0ms

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))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

526×	`*-un-lft-identity`
332×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
217×	`add-cube-cbrt`
156×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
22×	`frac-sub`
20×	`associate-/r*`
16×	`flip3-+` `flip-+` `div-inv`
13×	`flip3--` `flip--`
12×	`associate-/l*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `diff-log` `clear-num` `log1p-expm1-u`
3×	`sub-neg`
2×	`cbrt-undiv` `div-exp`
1×	`associate--r-`

Counts

4 → 433

Calls

4 calls:

40.0ms	(- (/ 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))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify108.0ms

Algorithm

egg-herbie

Counts

445 → 445

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1279	9130
1	5001	6953

prune660.0ms

Filtered

445 candidates to 218 candidates (49.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	440	5	445
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	450	7	457

Merged error: 3.1b

Counts

457 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series385.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (+ (+ alpha beta) 2.0))
101.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	453	1755
1	1246	1290
2	5001	1243

prune349.0ms

Filtered

164 candidates to 92 candidates (56.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	164	7	171

Merged error: 3.1b

Counts

171 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

216×	`*-un-lft-identity`
106×	`times-frac`
99×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
72×	`distribute-lft-out`
63×	`cbrt-prod` `prod-diff`
33×	`cbrt-div`
21×	`fma-neg`
15×	`associate-/r*`
14×	`associate-/r/`
9×	`associate-/l*`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`frac-2neg` `pow1/3` `clear-num`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 227

Calls

4 calls:

16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
153.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
151.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
157.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	523	2457
1	1484	1974
2	5001	1903

prune475.0ms

Filtered

239 candidates to 141 candidates (59.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	237	9	246

Merged error: 3.1b

Counts

246 → 9

regimes142.0ms

Accuracy

97.9% (0.3b remaining)

Error of 3.3b against oracle of 3.0b and baseline of 16.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

end0.0ms

sample595.0ms

Algorithm

intervals

Results

151.0ms	5823×	body	80	valid
104.0ms	885×	body	1280	valid
93.0ms	8000×	pre	80	true
69.0ms	718×	body	640	valid
26.0ms	369×	body	320	valid
10.0ms	205×	body	160	valid