Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	23×	body	1280	valid
2.0ms	22×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	8×	body	160	valid

simplify78.0ms

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: 15.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite35.0ms

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

series108.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

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

prune202.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 14.2b

Counts

107 → 11

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite97.0ms

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:

38.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify147.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (74.0ms)

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

prune619.0ms

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	8	2	10
Picked	1	0	1
Done	0	0	0
Total	425	11	436

Merged error: 2.9b

Counts

436 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (* (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
8.8b	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
8.8b	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
8.8b	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
63×	`cbrt-prod`
45×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `flip3-+` `pow1/3` `prod-diff` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 114

Calls

4 calls:

34.0ms	(- (* (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
7.0ms	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
143.0ms	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
148.0ms	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))
144.0ms	(cbrt (/ alpha (+ (+ alpha beta) 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	371	1369
1	1142	1166
2	5002	1093

prune384.0ms

Filtered

126 candidates to 94 candidates (74.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	126	11	137

Merged error: 2.9b

Counts

137 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite46.0ms

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)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
150.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
144.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
150.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (40.0ms)

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

prune408.0ms

Filtered

209 candidates to 120 candidates (57.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	212	8	220

Merged error: 2.9b

Counts

220 → 8

regimes93.0ms

Accuracy

77.3% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 15.6b

bsearch44.0ms

Steps

Iters	Range		Point
7	12753422947354472.0	5.168889984207901e+17	8.716404371789643e+16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	37
1	43	37

end0.0ms

sample630.0ms

Algorithm

intervals

Results

157.0ms	5866×	body	80	valid
101.0ms	811×	body	1280	valid
101.0ms	8000×	pre	80	true
83.0ms	780×	body	640	valid
27.0ms	360×	body	320	valid
9.0ms	183×	body	160	valid