Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	197×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
2.0ms	25×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite131.0ms

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))
99.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune217.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 179

Calls

3 calls:

19.0ms	(/ beta (+ (+ alpha beta) 2.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series172.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ beta (+ (+ alpha beta) 2.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	493	1766
1	1623	1302
2	5002	1263

prune340.0ms

Filtered

188 candidates to 97 candidates (51.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

0.0ms	(cbrt beta)
0.0ms	(cbrt beta)
1.0ms	(cbrt beta)
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series629.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt beta)
189.0ms	(cbrt beta)
181.0ms	(cbrt beta)
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	386	1443
1	1119	993
2	5001	940

prune344.0ms

Filtered

152 candidates to 82 candidates (53.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt beta))
0.6b	(cbrt (cbrt beta))
0.6b	(cbrt (cbrt beta))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 149

Calls

4 calls:

1.0ms	(cbrt (cbrt beta))
1.0ms	(cbrt (cbrt beta))
1.0ms	(cbrt (cbrt beta))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series808.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (cbrt beta))
243.0ms	(cbrt (cbrt beta))
242.0ms	(cbrt (cbrt beta))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	399	1554
1	1123	1098
2	5001	1039

prune601.0ms

Filtered

161 candidates to 88 candidates (54.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.4b

regimes69.0ms

Accuracy

67.8% (4.4b remaining)

Error of 7.3b against oracle of 2.9b and baseline of 16.5b

bsearch74.0ms

Steps

Iters	Range		Point
9	5.312605216618719e+48	4.3794405869739974e+54	5.368585705177939e+48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	52
1	51	52

end0.0ms

sample602.0ms

Algorithm

intervals

Results

148.0ms	5820×	body	80	valid
107.0ms	882×	body	1280	valid
95.0ms	8000×	pre	80	true
73.0ms	717×	body	640	valid
28.0ms	392×	body	320	valid
9.0ms	189×	body	160	valid