Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	191×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	26×	body	1280	valid
2.0ms	25×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	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: 15.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite230.0ms

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:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
177.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series94.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
54.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

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

prune212.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 229

Calls

4 calls:

1.2s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
36.0ms	(/ beta (+ (+ alpha beta) 2.0))
35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
219.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series215.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
41.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify86.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	714	2537
1	2533	2035
2	5001	2004

prune586.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(log1p (expm1 (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
91×	`times-frac`
86×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
12×	`associate-/r/`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `difference-of-squares`
1×	`sub-neg` `log1p-udef` `flip3--` `diff-log` `log1p-expm1` `flip--` `distribute-lft-out--`

Counts

4 → 190

Calls

4 calls:

37.0ms	(/ beta (+ (+ alpha beta) 2.0))
36.0ms	(/ alpha (+ (+ alpha beta) 2.0))
0.0ms	(log1p (expm1 (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
221.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series295.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ beta (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
141.0ms	(log1p (expm1 (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
69.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	519	1854
1	1680	1381
2	5001	1344

prune408.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.4b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.0s

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:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
356.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
213.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
407.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ alpha (+ (+ alpha beta) 2.0))
66.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
66.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	588	4260
1	1745	3041
2	5001	2291

prune445.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.3b

regimes98.0ms

Accuracy

70.4% (3.7b remaining)

Error of 7.0b against oracle of 3.3b and baseline of 15.9b

bsearch47.0ms

Steps

Iters	Range		Point
8	1.883147642109108e+44	5.1383985160358e+46	1.0243503852289514e+45

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample611.0ms

Algorithm

intervals

Results

142.0ms	5821×	body	80	valid
91.0ms	799×	body	1280	valid
90.0ms	8000×	pre	80	true
67.0ms	756×	body	640	valid
28.0ms	421×	body	320	valid
9.0ms	203×	body	160	valid