Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	182×	body	80	valid
4.0ms	32×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	25×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	7×	body	160	valid

simplify77.0ms

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	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: 17.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 121

Calls

3 calls:

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

series117.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(+ (+ alpha beta) 2.0)
49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
56.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	372	626
1	1272	594
2	5001	590

prune288.0ms

Filtered

130 candidates to 85 candidates (65.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	116	14	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	14	131

Merged error: 16.6b

Counts

131 → 14

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 413

Calls

4 calls:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
35.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
20.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series230.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ beta (+ (+ alpha beta) 2.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
57.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify137.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	977	8429
1	3143	6259
2	5002	6131

prune908.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	418	7	425
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	430	9	439

Merged error: 2.7b

Counts

439 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

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

series505.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
146.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
146.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
142.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	509	2277
1	1447	1794
2	5001	1714

prune525.0ms

Filtered

209 candidates to 120 candidates (57.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Merged error: 2.7b

Counts

218 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.8b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.0b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

465×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
252×	`prod-diff`
235×	`times-frac`
196×	`add-cube-cbrt`
126×	`distribute-lft-out`
65×	`associate--r+`
50×	`difference-of-squares`
42×	`fma-neg`
31×	`distribute-lft-out--`
28×	`associate-/r/`
14×	`log-prod` `flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
8×	`log-div`
7×	`flip3--` `exp-sum` `flip--`
6×	`pow1` `frac-sub`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `diff-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg`
2×	`log-pow`
1×	`rem-log-exp` `rem-exp-log` `associate--r-`

Counts

4 → 382

Calls

4 calls:

34.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
26.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
30.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
63.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
125.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify131.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	968	8783
1	2828	6586
2	5002	6436

prune806.0ms

Filtered

394 candidates to 189 candidates (48.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	389	5	394
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	393	10	403

Merged error: 2.7b

Counts

403 → 10

regimes100.0ms

Accuracy

75.2% (3.2b remaining)

Error of 6.1b against oracle of 2.9b and baseline of 15.9b

bsearch39.0ms

Steps

Iters	Range		Point
5	6117620759736144.0	16816149477681434.0	15329950251265012.0

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	55
1	49	55

end0.0ms

sample597.0ms

Algorithm

intervals

Results

148.0ms	5840×	body	80	valid
114.0ms	882×	body	1280	valid
92.0ms	8000×	pre	80	true
64.0ms	680×	body	640	valid
27.0ms	379×	body	320	valid
10.0ms	219×	body	160	valid