Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	183×	body	80	valid
6.0ms	32×	body	1280	valid
5.0ms	256×	pre	80	true
4.0ms	26×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify77.0ms

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: 17.2b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite129.0ms

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
100.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series105.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune206.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.4b

localize11.0ms

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

rewrite487.0ms

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:

301.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series223.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify133.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

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

prune715.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.5b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite158.0ms

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:

118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
146.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
140.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
148.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (38.0ms)

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

prune510.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.5b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

345×	`*-un-lft-identity`
221×	`add-sqr-sqrt`
216×	`times-frac`
165×	`add-cube-cbrt`
126×	`prod-diff`
102×	`distribute-lft-out`
61×	`sqrt-prod`
42×	`fma-neg`
30×	`add-exp-log` `associate-r` `associate-l`
22×	`associate-/r/`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
11×	`flip3-+` `flip-+` `div-inv`
10×	`div-exp`
8×	`pow1` `prod-exp` `associate-/r*` `add-log-exp`
6×	`sqrt-div`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`rec-exp` `pow-flip` `1-exp` `associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`frac-times` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 360

Calls

4 calls:

101.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
19.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series285.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
70.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify108.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	859	4332
1	3759	3194
2	5001	2935

prune667.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes129.0ms

Accuracy

76.9% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.6b

bsearch75.0ms

Steps

Iters	Range		Point
9	531.7447489915417	834758988592.4675	818395241689.5887

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	39
1	49	39

end0.0ms

sample972.0ms

Algorithm

intervals

Results

326.0ms	5858×	body	80	valid
164.0ms	891×	body	1280	valid
157.0ms	8000×	pre	80	true
111.0ms	687×	body	640	valid
45.0ms	376×	body	320	valid
16.0ms	188×	body	160	valid