Details

sample27.0ms

Algorithm

intervals

Results

5.0ms	185×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	29×	body	1280	valid
2.0ms	19×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify78.0ms

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: 16.7b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- 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:

14.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
20.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series105.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
57.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune194.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	92	14	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	14	107

Merged error: 16.0b

Counts

107 → 14

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	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite106.0ms

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:

36.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
12.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series230.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ beta (+ (+ alpha beta) 2.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
73.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify146.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (75.0ms)

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

prune613.0ms

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	11	2	13
Picked	1	0	1
Done	0	0	0
Total	428	11	439

Merged error: 2.6b

Counts

439 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.2b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

280×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
137×	`times-frac`
131×	`add-cube-cbrt`
126×	`prod-diff`
87×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg`
18×	`associate-/r/`
10×	`associate-/r*`
9×	`flip3-+` `flip-+` `div-inv`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 265

Calls

4 calls:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
20.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ beta (+ (+ alpha beta) 2.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
80.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	632	3075
1	1864	2160
2	5002	1838

prune377.0ms

Filtered

277 candidates to 126 candidates (45.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	276	1	277
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	277	11	288

Merged error: 2.6b

Counts

288 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
2.2b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity`
131×	`times-frac`
89×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`pow1`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 210

Calls

4 calls:

8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
32.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
18.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series329.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
133.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
56.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
92.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify123.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	790	2498
1	4019	2269
2	5002	2219

prune387.0ms

Filtered

222 candidates to 135 candidates (60.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	222	11	233

Merged error: 2.6b

Counts

233 → 11

regimes116.0ms

Accuracy

77.1% (2.8b remaining)

Error of 5.6b against oracle of 2.7b and baseline of 15.2b

bsearch54.0ms

Steps

Iters	Range		Point
9	1764672.720573475	49271540691113.9	43326542873974.99

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample707.0ms

Algorithm

intervals

Results

186.0ms	5918×	body	80	valid
127.0ms	8000×	pre	80	true
119.0ms	808×	body	1280	valid
81.0ms	709×	body	640	valid
34.0ms	363×	body	320	valid
12.0ms	202×	body	160	valid