Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	194×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	27×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	8×	body	160	valid

simplify82.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- 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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune243.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite109.0ms

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:

9.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
58.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify141.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (73.0ms)

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

prune786.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
5.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.3b	(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)
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
12.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
151.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
143.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
154.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (40.0ms)

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

prune521.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.7b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 187

Calls

4 calls:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
28.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
22.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
32.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ beta (+ (+ alpha beta) 2.0))
65.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
133.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	666	2336
1	2236	1838
2	5002	1790

prune432.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

regimes108.0ms

Accuracy

77.7% (3.0b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 16.4b

bsearch47.0ms

Steps

Iters	Range		Point
7	99314083682.35872	1732166801363.969	410714263654.7934

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	34
1	55	34
2	55	34

end0.0ms

sample690.0ms

Algorithm

intervals

Results

168.0ms	5813×	body	80	valid
129.0ms	886×	body	1280	valid
109.0ms	8000×	pre	80	true
80.0ms	704×	body	640	valid
33.0ms	395×	body	320	valid
14.0ms	202×	body	160	valid