Details

sample27.0ms

Algorithm

intervals

Results

5.0ms	182×	body	80	valid
4.0ms	32×	body	1280	valid
3.0ms	256×	pre	80	true
3.0ms	25×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	7×	body	160	valid

simplify123.0ms

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: 17.3b

Counts

2 → 1

localize9.0ms

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)

rewrite53.0ms

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` `+-commutative` `expm1-log1p-u` `log1p-expm1-u`
2×	`associate-+l+` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`

Counts

3 → 122

Calls

3 calls:

6.0ms	(+ (+ alpha beta) 2.0)
12.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
30.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series135.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ (+ alpha beta) 2.0)
49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
71.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	373	627
1	1270	595
2	5001	591

prune330.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	117	14	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	14	132

Merged error: 16.6b

Counts

132 → 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)

rewrite111.0ms

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:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series268.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ beta (+ (+ alpha beta) 2.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
74.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
94.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify109.0ms

Algorithm

egg-herbie

Counts

445 → 445

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1286	9129
1	5001	6953

prune886.0ms

Filtered

445 candidates to 218 candidates (49.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	438	7	445
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	450	9	459

Merged error: 2.7b

Counts

459 → 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)))

rewrite57.0ms

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:

22.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
160.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
144.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
155.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	530	2457
1	1540	1974
2	5001	1885

prune633.0ms

Filtered

239 candidates to 138 candidates (57.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	239	9	248

Merged error: 2.7b

Counts

248 → 9

localize13.0ms

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)))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

507×	`*-un-lft-identity`
333×	`add-sqr-sqrt`
252×	`prod-diff`
235×	`times-frac`
208×	`add-cube-cbrt`
144×	`distribute-lft-out`
66×	`frac-sub`
65×	`associate--r+`
50×	`difference-of-squares`
48×	`log-div`
42×	`fma-neg`
37×	`flip3--` `flip--`
31×	`distribute-lft-out--`
30×	`associate-/r*`
28×	`associate-/r/`
24×	`exp-diff`
18×	`associate-/l*`
14×	`log-prod` `flip3-+` `flip-+` `div-inv`
12×	`add-log-exp`
7×	`exp-sum`
6×	`pow1` `frac-2neg` `clear-num`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `diff-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg`
2×	`log-pow` `rem-exp-log`
1×	`rem-log-exp` `associate--r-`

Counts

4 → 443

Calls

4 calls:

39.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
246.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
35.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
61.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
73.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
127.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify120.0ms

Algorithm

egg-herbie

Counts

455 → 455

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1357	10953
1	5001	8726

prune974.0ms

Filtered

455 candidates to 225 candidates (49.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	449	6	455
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	454	10	464

Merged error: 2.7b

Counts

464 → 10

regimes120.0ms

Accuracy

75.2% (3.2b remaining)

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

bsearch35.0ms

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

sample618.0ms

Algorithm

intervals

Results

154.0ms	5840×	body	80	valid
117.0ms	882×	body	1280	valid
96.0ms	8000×	pre	80	true
71.0ms	680×	body	640	valid
29.0ms	379×	body	320	valid
11.0ms	219×	body	160	valid