Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	188×	body	80	valid
4.0ms	30×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	4×	body	160	valid

simplify80.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite126.0ms

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:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
97.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series109.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune210.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.0b

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))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite488.0ms

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:

18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
301.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
20.0ms	(/ beta (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series229.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
60.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify134.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

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

prune714.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.1b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite572.0ms

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

series267.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
74.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	638	4268
1	1852	3053
2	5002	2419

prune471.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.1b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

232×	`*-un-lft-identity`
126×	`prod-diff`
123×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
107×	`times-frac`
69×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg`
14×	`associate-/r/`
10×	`cbrt-prod`
9×	`flip3-+` `flip-+`
7×	`log-pow` `div-inv`
6×	`exp-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `pow1/3` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 221

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
224.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series346.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (+ alpha beta) 2.0))
95.0ms	(cbrt (+ (+ alpha beta) 2.0))
76.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	599	2917
1	1546	2012
2	5002	1578

prune493.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

regimes101.0ms

Accuracy

70.5% (3.8b remaining)

Error of 6.8b against oracle of 3.1b and baseline of 15.8b

bsearch49.0ms

Steps

Iters	Range		Point
7	1.2675713909696286e+39	2.5917733915296634e+41	1.2077500397799626e+40

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	38
1	44	38

end0.0ms

sample618.0ms

Algorithm

intervals

Results

154.0ms	5836×	body	80	valid
104.0ms	833×	body	1280	valid
96.0ms	8000×	pre	80	true
70.0ms	725×	body	640	valid
34.0ms	424×	body	320	valid
9.0ms	182×	body	160	valid