Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	189×	body	80	valid
3.0ms	28×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	7×	body	160	valid

simplify83.0ms

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 (100.0%)

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: 15.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- 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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series120.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
67.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	329	555
1	1066	529
2	5002	525

prune177.0ms

Filtered

106 candidates to 68 candidates (35.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 14.9b

Counts

107 → 10

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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

322×	`*-un-lft-identity`
170×	`add-sqr-sqrt`
161×	`times-frac`
145×	`add-cube-cbrt`
126×	`prod-diff`
93×	`distribute-lft-out`
66×	`div-sub`
65×	`associate--r+`
24×	`associate-/l/`
23×	`associate-/r*`
22×	`frac-sub`
21×	`fma-neg`
19×	`associate-/l*`
18×	`associate-/r/`
13×	`flip3--` `flip--` `distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube` `div-inv` `difference-of-squares`
9×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`frac-2neg` `clear-num`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`sub-neg`
1×	`diff-log`

Counts

4 → 314

Calls

4 calls:

57.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series259.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
85.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify131.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	1135	4337
1	3862	3531
2	5001	3527

prune472.0ms

Filtered

326 candidates to 165 candidates (49.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	318	8	326
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	325	11	336

Merged error: 3.3b

Counts

336 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.2b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite73.0ms

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×	`add-exp-log` `flip3-+` `flip-+` `div-inv`
8×	`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` `rem-log-exp` `clear-num` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `flip--`

Counts

4 → 266

Calls

4 calls:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
20.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
22.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series278.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ beta (+ (+ alpha beta) 2.0))
55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
85.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
84.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	627	3076
1	1823	2160
2	5002	1838

prune392.0ms

Filtered

278 candidates to 126 candidates (54.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	278	11	289

Merged error: 3.3b

Counts

289 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.2b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite69.0ms

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` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `pow1/3` `rem-log-exp` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `flip--`

Counts

4 → 222

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
6.0ms	(cbrt (+ (+ alpha beta) 2.0))
25.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series385.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (+ (+ alpha beta) 2.0))
107.0ms	(cbrt (+ (+ alpha beta) 2.0))
84.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
87.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify79.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	592	2917
1	1487	2012
2	5001	1584

prune446.0ms

Filtered

234 candidates to 107 candidates (54.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	231	3	234
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	235	10	245

Merged error: 3.3b

Counts

245 → 10

regimes165.0ms

Accuracy

98.3% (0.2b remaining)

Error of 3.3b against oracle of 3.0b and baseline of 16.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	56
1	49	56

end0.0ms

sample622.0ms

Algorithm

intervals

Results

154.0ms	5773×	body	80	valid
107.0ms	855×	body	1280	valid
101.0ms	8000×	pre	80	true
74.0ms	768×	body	640	valid
29.0ms	397×	body	320	valid
10.0ms	207×	body	160	valid