Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	183×	body	80	valid
3.0ms	37×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	18×	body	1280	valid
1.0ms	12×	body	320	valid
0.0ms	6×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite137.0ms

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:

26.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
106.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series116.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- 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 (30.0ms)

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

prune239.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.4b

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))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite528.0ms

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:

327.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
129.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify137.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (71.0ms)

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

prune799.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.8b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite434.0ms

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:

19.0ms	(/ beta (+ (+ alpha beta) 2.0))
20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
246.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
129.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series258.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ beta (+ (+ alpha beta) 2.0))
51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
83.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify81.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	632	3075
1	1862	2160
2	5001	1838

prune506.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.1b	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
1.8b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
139×	`times-frac`
131×	`add-cube-cbrt`
126×	`prod-diff`
84×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg` `associate-r`
18×	`associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3-+` `flip-+` `div-inv`
8×	`pow1`
7×	`log-pow`
6×	`exp-prod` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`log-div` `flip3--` `pow-flip` `frac-2neg` `exp-diff` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `flip--` `inv-pow`

Counts

4 → 276

Calls

4 calls:

21.0ms	(/ 1 (+ (+ alpha beta) 2.0))
49.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
243.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
128.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series259.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (+ (+ alpha beta) 2.0))
53.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
82.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
87.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	717	3114
1	2406	2159
2	5001	1798

prune500.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

regimes128.0ms

Accuracy

77.8% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 15.9b

bsearch59.0ms

Steps

Iters	Range		Point
8	523281070680199.5	9.528795435980767e+18	25643285862390824.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	25
1	38	25

end0.0ms

sample602.0ms

Algorithm

intervals

Results

145.0ms	5813×	body	80	valid
104.0ms	851×	body	1280	valid
98.0ms	8000×	pre	80	true
70.0ms	746×	body	640	valid
27.0ms	379×	body	320	valid
13.0ms	211×	body	160	valid