Details

sample40.0ms

Algorithm

intervals

Results

11.0ms	195×	body	80	valid
7.0ms	18×	body	640	valid
6.0ms	22×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify71.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 65

Calls

2 calls:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
87.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune159.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.6b

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	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

228.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series228.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune298.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.3b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite414.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
139×	`times-frac`
89×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
48×	`distribute-lft-out`
24×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
8×	`div-exp` `div-inv`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `diff-log`
3×	`sub-neg` `flip3--` `associate-/r/` `flip--`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub` `associate--r+`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow` `associate--r-`

Counts

4 → 179

Calls

4 calls:

264.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
24.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series274.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
56.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	677	1657
1	2938	1424
2	5001	1418

prune309.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

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))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

9.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series373.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	278	567
1	708	537
2	2658	521
3	5001	512

prune267.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

regimes166.0ms

Accuracy

98% (0.3b remaining)

Error of 3.3b against oracle of 3.0b and baseline of 16.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	28
1	43	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

325.0ms	5789×	body	80	valid
229.0ms	862×	body	1280	valid
160.0ms	748×	body	640	valid
130.0ms	8000×	pre	80	true
67.0ms	398×	body	320	valid
24.0ms	203×	body	160	valid