Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample58.0ms

Algorithm

intervals

Results

15.0ms	256×	pre	80	true
13.0ms	189×	body	80	valid
7.0ms	24×	body	1280	valid
5.0ms	22×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5003	19

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite32.0ms

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

series25.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
13.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify79.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5371	1505

prune179.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 14.9b

Counts

72 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ beta alpha) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0))
1.5b	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)

rewrite72.0ms

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`
1×	`associate--r+` `associate--r-`

Counts

4 → 108

Calls

4 calls:

11.0ms	(/ alpha (+ (+ beta alpha) 2.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
31.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0))
14.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)

series48.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ alpha (+ (+ beta alpha) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0))
18.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4979	2498
1	4979	2498

prune228.0ms

Filtered

87 candidates to 120 candidates (-37.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	121	10	131

Merged error: 2.6b

Counts

131 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
6.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 104

Calls

4 calls:

20.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
34.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
26.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
23.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify103.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4930	2636
1	4930	2636

prune451.0ms

Filtered

92 candidates to 116 candidates (-26.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 2.6b

Counts

126 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.5b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.8b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
14×	`log-prod`
11×	`add-log-exp`
10×	`distribute-lft-out--`
8×	`log-div` `difference-of-squares`
7×	`add-cube-cbrt` `flip3--` `exp-sum` `flip--`
6×	`pow1` `frac-sub`
5×	`add-exp-log`
4×	`exp-prod` `times-frac` `exp-diff` `diff-log` `add-cbrt-cube`
3×	`sub-neg`
2×	`log-pow`
1×	`rem-log-exp` `rem-exp-log` `associate--r+` `associate--r-`

Counts

4 → 77

Calls

4 calls:

31.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
28.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
27.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
28.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
24.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
23.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
39.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify160.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4898	3150
1	4898	3150

prune238.0ms

Filtered

72 candidates to 89 candidates (-23.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	88	9	97

Merged error: 2.6b

Counts

97 → 9

regimes222.0ms

Accuracy

77.6% (2.9b remaining)

Error of 5.8b against oracle of 2.9b and baseline of 15.9b

bsearch39.0ms

Steps

Iters	Range		Point
9	40817232.135885924	1.0382314314237171e+17	218152260.39439523

simplify30.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	723	152
1	723	152

end0.0ms

sample932.0ms

Algorithm

intervals

Results

240.0ms	5817×	body	80	valid
181.0ms	849×	body	1280	valid
158.0ms	8000×	pre	80	true
114.0ms	718×	body	640	valid
47.0ms	386×	body	320	valid
19.0ms	230×	body	160	valid

Details

analyze5.0ms

sample58.0ms

simplify93.0ms

prune5.0ms

localize8.0ms

rewrite32.0ms

series25.0ms

simplify79.0ms

prune179.0ms

localize13.0ms

rewrite72.0ms

series48.0ms

simplify64.0ms

prune228.0ms

localize27.0ms

rewrite54.0ms

series98.0ms

simplify103.0ms

prune451.0ms

localize21.0ms

rewrite118.0ms

series110.0ms

simplify160.0ms

prune238.0ms

regimes222.0ms

bsearch39.0ms

simplify30.0ms

end0.0ms

sample932.0ms

Profiling