Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	186×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	29×	body	1280	valid
2.0ms	19×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	4×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.8b

Counts

2 → 1

localize7.0ms

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)

rewrite37.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
23.0ms	(+ (/ (- 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)

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune198.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 16.0b

Counts

107 → 11

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)

rewrite103.0ms

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:

34.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
10.0ms	(/ alpha (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify145.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (75.0ms)

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

prune592.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	418	7	425
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	429	7	436

Merged error: 2.7b

Counts

436 → 7

localize12.0ms

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

rewrite89.0ms

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:

17.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
20.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
19.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series262.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
74.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
70.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify86.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (48.0ms)

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

prune392.0ms

Filtered

321 candidates to 125 candidates (38.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	321	0	321
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	321	7	328

Merged error: 2.7b

Counts

328 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series368.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (+ (+ alpha beta) 2.0))
94.0ms	(cbrt (+ (+ alpha beta) 2.0))
95.0ms	(cbrt (+ (+ alpha beta) 2.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	460	1755
1	1302	1290
2	5001	1240

prune351.0ms

Filtered

164 candidates to 90 candidates (54.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	163	8	171

Merged error: 2.7b

Counts

171 → 8

regimes112.0ms

Accuracy

73.3% (3.4b remaining)

Error of 6.5b against oracle of 3.1b and baseline of 15.7b

bsearch85.0ms

Steps

Iters	Range		Point
4	8.85312560244671e+136	1.6661249883901243e+137	1.2790061907342682e+137
8	3.1357525583305223e+117	2.3462675926281506e+120	4.535383575684779e+119
0	1596871.5183753124	1650110.102945949	1623490.8106606307

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	54
1	55	54

end0.0ms

sample597.0ms

Algorithm

intervals

Results

142.0ms	5837×	body	80	valid
112.0ms	856×	body	1280	valid
94.0ms	8000×	pre	80	true
66.0ms	712×	body	640	valid
29.0ms	377×	body	320	valid
10.0ms	218×	body	160	valid