Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	188×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	26×	body	1280	valid
3.0ms	28×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	2×	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: 16.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite127.0ms

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))
97.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series104.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
57.0ms	(+ (/ (- 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

prune211.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite475.0ms

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:

17.0ms	(/ beta (+ (+ alpha beta) 2.0))
297.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series234.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ beta (+ (+ alpha beta) 2.0))
57.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify136.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (69.0ms)

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

prune731.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.9b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite575.0ms

Algorithm

rewrite-expression-head

Rules

346×	`*-un-lft-identity`
189×	`prod-diff`
185×	`add-sqr-sqrt`
170×	`add-cube-cbrt`
168×	`times-frac`
130×	`exp-sum`
102×	`distribute-lft-out`
68×	`log-prod`
22×	`associate-/r/`
21×	`fma-neg`
12×	`exp-prod`
11×	`flip3-+` `flip-+` `div-inv`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 309

Calls

4 calls:

197.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
220.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series266.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
73.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify78.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	588	4260
1	1743	3041
2	5002	2399

prune456.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
130×	`add-sqr-sqrt`
126×	`prod-diff`
122×	`times-frac`
120×	`add-cube-cbrt`
78×	`distribute-lft-out`
42×	`fma-neg`
16×	`associate-/r/`
10×	`cbrt-prod` `flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 236

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series363.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (+ alpha beta) 2.0))
101.0ms	(cbrt (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
85.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	460	2922
1	1302	2024
2	5001	1948

prune573.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

regimes88.0ms

Accuracy

74.4% (3.4b remaining)

Error of 6.4b against oracle of 3.0b and baseline of 16.3b

bsearch51.0ms

Steps

Iters	Range		Point
8	1.4366889122671085e+27	3.2593449619462425e+30	4.836259073578557e+29

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	29
1	40	29

end0.0ms

sample608.0ms

Algorithm

intervals

Results

151.0ms	5765×	body	80	valid
103.0ms	855×	body	1280	valid
97.0ms	8000×	pre	80	true
75.0ms	733×	body	640	valid
32.0ms	436×	body	320	valid
10.0ms	211×	body	160	valid