Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	200×	body	80	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	1280	valid
2.0ms	20×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	4×	body	160	valid

simplify73.0ms

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: 13.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite115.0ms

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
87.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series109.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune148.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

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))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite369.0ms

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:

229.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

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

prune281.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.8b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
148×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
60×	`distribute-lft-out`
27×	`associate-/r*`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
7×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `associate-/l/` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 189

Calls

4 calls:

36.0ms	(/ (+ (+ alpha beta) 2.0) beta)
19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
22.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (+ (+ alpha beta) 2.0) beta)
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
58.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	586	1449
1	2527	1314
2	5001	1211

prune322.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.3b	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
4.3b	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
4.3b	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

307×	`times-frac`
282×	`*-un-lft-identity`
186×	`cbrt-prod`
150×	`add-sqr-sqrt`
145×	`add-cube-cbrt`
81×	`distribute-lft-out`
12×	`div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `pow1/3` `associate-/r/`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 228

Calls

4 calls:

100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
17.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
14.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
15.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
156.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
152.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
158.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))

simplify71.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	535	3105
1	1762	2931
2	5001	2611

prune388.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

regimes114.0ms

Accuracy

78.3% (2.8b remaining)

Error of 5.9b against oracle of 3.2b and baseline of 15.9b

bsearch48.0ms

Steps

Iters	Range		Point
8	60.984244775781654	93455.48925387283	92108.89598052698

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	27
1	43	27

end0.0ms

sample605.0ms

Algorithm

intervals

Results

150.0ms	5846×	body	80	valid
102.0ms	855×	body	1280	valid
100.0ms	8000×	pre	80	true
66.0ms	690×	body	640	valid
28.0ms	401×	body	320	valid
10.0ms	208×	body	160	valid