Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
5.0ms	30×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	22×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	10×	body	160	valid

simplify76.0ms

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: 16.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite35.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
58.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

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

prune144.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 16.1b

Counts

72 → 12

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	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

30.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5002	1268

prune293.0ms

Filtered

149 candidates to 103 candidates (69.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	8	149
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	153	8	161

Merged error: 2.9b

Counts

161 → 8

localize18.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite32.0ms

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:

6.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
14.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series379.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (67.0ms)

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

prune245.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 2.9b

Counts

80 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.7b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.6b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
64×	`times-frac`
50×	`log-prod`
37×	`add-cube-cbrt`
25×	`exp-sum`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
12×	`distribute-lft-out`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod`
3×	`div-inv` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `associate-/r/` `log-pow`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `clear-num` `flip--` `flip-+` `rem-exp-log`

Counts

4 → 126

Calls

4 calls:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
29.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
27.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series331.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ beta (+ (+ alpha beta) 2.0))
69.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
136.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	548	1697
1	1594	1612
2	5002	1558

prune287.0ms

Filtered

138 candidates to 95 candidates (68.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Merged error: 2.9b

Counts

144 → 10

regimes101.0ms

Accuracy

75.8% (3.2b remaining)

Error of 5.9b against oracle of 2.7b and baseline of 16.0b

bsearch57.0ms

Steps

Iters	Range		Point
8	141.1477961436799	700452.7431191434	687925.8537243882

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	38
1	48	38

end0.0ms

sample722.0ms

Algorithm

intervals

Results

181.0ms	5837×	body	80	valid
143.0ms	884×	body	1280	valid
125.0ms	8000×	pre	80	true
84.0ms	694×	body	640	valid
36.0ms	393×	body	320	valid
12.0ms	192×	body	160	valid

Details

sample28.0ms

simplify76.0ms

prune2.0ms

localize8.0ms

rewrite35.0ms

series108.0ms

simplify39.0ms

prune144.0ms

localize9.0ms

rewrite68.0ms

series241.0ms

simplify58.0ms

prune293.0ms

localize18.0ms

rewrite32.0ms

series379.0ms

simplify74.0ms

prune245.0ms

localize13.0ms

rewrite87.0ms

series331.0ms

simplify54.0ms

prune287.0ms

regimes101.0ms

bsearch57.0ms

simplify2.0ms

end0.0ms

sample722.0ms

Profiling