Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	182×	body	80	valid
4.0ms	32×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	25×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	7×	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	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	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: 17.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ alpha beta) 2.0)
0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`distribute-lft-out`
15×	`add-cube-cbrt`
10×	`add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`sum-log`
3×	`pow1` `+-commutative` `flip3-+` `flip-+`
2×	`associate-+l+` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`

Counts

3 → 81

Calls

3 calls:

6.0ms	(+ (+ alpha beta) 2.0)
14.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series116.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(+ (+ alpha beta) 2.0)
48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
56.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	354	601
1	1199	571
2	5002	567

prune187.0ms

Filtered

90 candidates to 59 candidates (65.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	13	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	13	91

Merged error: 16.6b

Counts

91 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
32×	`times-frac`
30×	`distribute-lft-out`
28×	`add-cube-cbrt`
22×	`frac-sub`
20×	`associate-/r*`
13×	`flip3--` `flip--`
12×	`associate-/l*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `frac-2neg` `diff-log` `clear-num` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg`
2×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 131

Calls

4 calls:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
10.0ms	(/ alpha (+ (+ alpha beta) 2.0))
31.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ beta (+ (+ alpha beta) 2.0))
55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
57.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	748	1633
1	3482	1592
2	5001	1592

prune354.0ms

Filtered

143 candidates to 96 candidates (67.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	8	143
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	148	8	156

Merged error: 2.7b

Counts

156 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.3b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
42×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
36×	`distribute-lft-out`
33×	`cbrt-div`
15×	`associate-/r*`
9×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`frac-2neg` `flip3-+` `pow1/3` `clear-num` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 135

Calls

4 calls:

15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
152.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
146.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
142.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify173.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 3 (152.0ms)

Iter	Nodes	Cost
0	354	1257
1	985	1209
2	4544	1172
3	5002	1154

prune463.0ms

Filtered

147 candidates to 104 candidates (70.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	147	8	155

Merged error: 2.7b

Counts

155 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ beta (sqrt (+ (+ alpha beta) 2.0))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.1b	(/ (- (* (/ beta (sqrt (+ (+ alpha beta) 2.0))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (sqrt (+ (+ alpha beta) 2.0)) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
2.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite16.8s

Algorithm

rewrite-expression-head

Rules

88348×	`frac-times`
68401×	`*-un-lft-identity`
54246×	`associate-/r*`
40020×	`frac-add`
35154×	`associate-/l/`
35152×	`frac-sub`
33625×	`flip3-+` `flip-+`
28081×	`associate-/l*`
27962×	`distribute-lft-out`
26954×	`sqrt-div`
22514×	`add-sqr-sqrt`
21299×	`add-cube-cbrt`
15324×	`associate-*r/`
13502×	`sqrt-prod`
13184×	`flip3--` `flip--`
12242×	`associate-*l/`
9539×	`clear-num`
9263×	`frac-2neg`
882×	`associate-/r/`
614×	`times-frac`
552×	`un-div-inv`
434×	`unswap-sqr`
355×	`associate-l`
300×	`difference-of-squares`
173×	`associate-r`
97×	`distribute-lft-out--`
21×	`*-commutative`
18×	`unpow-prod-down` `cube-prod`
16×	`add-exp-log` `add-cbrt-cube`
10×	`sqr-pow`
6×	`pow1` `distribute-rgt-in` `distribute-lft-in` `add-log-exp`
5×	`div-sub`
4×	`difference-cubes` `cbrt-undiv` `+-commutative` `pow-unpow` `associate-+r+` `div-exp` `associate--r+`
3×	`sub-neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`diff-log` `pow-prod-down`

Counts

4 → 41065

Calls

4 calls:

294.0ms	(* (/ beta (sqrt (+ (+ alpha beta) 2.0))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
5.2s	(/ (- (* (/ beta (sqrt (+ (+ alpha beta) 2.0))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (sqrt (+ (+ alpha beta) 2.0)) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (sqrt (+ (+ alpha beta) 2.0))))
9.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
49.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series935.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (/ beta (sqrt (+ (+ alpha beta) 2.0))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
547.0ms	(/ (- (* (/ beta (sqrt (+ (+ alpha beta) 2.0))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (sqrt (+ (+ alpha beta) 2.0)) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (sqrt (+ (+ alpha beta) 2.0))))
77.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
107.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify22.2s

Algorithm

egg-herbie

Counts

41077 → 41077

Iterations

Useful iterations: 0 (315.0ms)

Iter	Nodes	Cost
0	22023	2430335

prune3.6m

Filtered

41077 candidates to 17094 candidates (41.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	41072	5	41077
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	41075	10	41085

Merged error: 2.7b

Counts

41085 → 10

regimes146.0ms

Accuracy

75.3% (3.2b remaining)

Error of 6.1b against oracle of 2.9b and baseline of 15.9b

bsearch36.0ms

Steps

Iters	Range		Point
5	6117620759736144.0	16816149477681434.0	15329950251265012.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample632.0ms

Algorithm

intervals

Results

154.0ms	5840×	body	80	valid
119.0ms	882×	body	1280	valid
103.0ms	8000×	pre	80	true
69.0ms	680×	body	640	valid
29.0ms	379×	body	320	valid
11.0ms	219×	body	160	valid