Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	197×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	20×	body	1280	valid
2.0ms	19×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	6×	body	160	valid

simplify79.0ms

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: 13.5b

Counts

2 → 1

localize8.0ms

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)

rewrite43.0ms

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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
26.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series112.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	335	555
1	1087	529
2	5002	525

prune198.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 12.6b

Counts

107 → 10

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)

rewrite107.0ms

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:

43.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series443.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
285.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify145.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (76.0ms)

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

prune629.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	416	9	425
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	424	11	435

Merged error: 4.4b

Counts

435 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
4.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
4.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite56.0ms

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:

17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
12.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
149.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
144.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
154.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (41.0ms)

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

prune420.0ms

Filtered

209 candidates to 120 candidates (57.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	211	9	220

Merged error: 4.4b

Counts

220 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.8b	(log (exp (/ beta (+ (+ alpha beta) 2.0))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

208×	`*-un-lft-identity`
106×	`times-frac`
96×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
69×	`distribute-lft-out`
63×	`prod-diff`
22×	`log-pow`
21×	`exp-prod` `fma-neg`
14×	`associate-/r/`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `distribute-lft-out--`

Counts

4 → 214

Calls

4 calls:

8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
15.0ms	(log (exp (/ beta (+ (+ alpha beta) 2.0))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
53.0ms	(log (exp (/ beta (+ (+ alpha beta) 2.0))))

simplify67.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	545	1937
1	1703	1460
2	5002	1422

prune360.0ms

Filtered

226 candidates to 124 candidates (54.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	226	9	235

Merged error: 4.4b

Counts

235 → 9

regimes89.0ms

Accuracy

73.8% (3.4b remaining)

Error of 6.4b against oracle of 3.0b and baseline of 16.0b

bsearch64.0ms

Steps

Iters	Range		Point
8	5.874928139471969e+33	2.2452270734650783e+36	8.430079037037424e+35

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	35
1	40	35

end0.0ms

sample758.0ms

Algorithm

intervals

Results

193.0ms	5869×	body	80	valid
149.0ms	878×	body	1280	valid
126.0ms	8000×	pre	80	true
87.0ms	687×	body	640	valid
37.0ms	367×	body	320	valid
16.0ms	199×	body	160	valid