Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	180×	body	80	valid
4.0ms	31×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	25×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	5×	body	160	valid

simplify77.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite139.0ms

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:

27.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
107.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series106.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- 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

prune215.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.9b

localize10.0ms

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))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite542.0ms

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:

336.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
20.0ms	(/ beta (+ (+ alpha beta) 2.0))
134.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify132.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

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

prune742.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(fma beta (/ 1 (+ (+ alpha beta) 2.0)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
91×	`times-frac`
86×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
12×	`associate-/r/`
10×	`add-exp-log` `associate-/r*`
8×	`add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`div-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `rec-exp` `flip3--` `pow-flip` `diff-log` `1-exp` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow`

Counts

4 → 193

Calls

4 calls:

21.0ms	(/ 1 (+ (+ alpha beta) 2.0))
21.0ms	(/ alpha (+ (+ alpha beta) 2.0))
0.0ms	(fma beta (/ 1 (+ (+ alpha beta) 2.0)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
132.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series223.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1 (+ (+ alpha beta) 2.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
62.0ms	(fma beta (/ 1 (+ (+ alpha beta) 2.0)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	528	1911
1	1812	1414
2	5003	1356

prune356.0ms

Filtered

205 candidates to 103 candidates (50.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
36×	`distribute-lft-out`
21×	`fma-neg`
9×	`cbrt-prod`
8×	`associate-/r/`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
133.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series614.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt beta)
177.0ms	(cbrt beta)
186.0ms	(cbrt beta)
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	386	1443
1	1119	993
2	5001	940

prune282.0ms

Filtered

152 candidates to 82 candidates (53.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

regimes64.0ms

Accuracy

75.1% (3.2b remaining)

Error of 6.1b against oracle of 2.9b and baseline of 15.8b

bsearch24.0ms

Steps

Iters	Range		Point
3	35727942855918572.0	4.564364949752027e+16	3.73426938437445e+16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	31
1	43	31

end0.0ms

sample637.0ms

Algorithm

intervals

Results

157.0ms	5851×	body	80	valid
113.0ms	859×	body	1280	valid
103.0ms	8000×	pre	80	true
81.0ms	741×	body	640	valid
28.0ms	373×	body	320	valid
9.0ms	176×	body	160	valid