Details

analyze3.0ms

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

sample25.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	23×	body	1280	valid
2.0ms	19×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	11×	body	160	valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5002	13

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: 14.4b

Counts

2 → 1

localize9.0ms

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)

rewrite34.0ms

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

series19.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
12.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5370	1005

prune129.0ms

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: 13.6b

Counts

72 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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:

25.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series41.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	6016	1670

prune202.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Merged error: 3.4b

Counts

131 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.0b	(/ 1 (+ alpha (+ beta 2.0)))
0.1b	(* beta (/ 1 (+ alpha (+ beta 2.0))))
2.1b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
48×	`times-frac`
46×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
33×	`distribute-lft-out`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/r*`
7×	`pow1`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 136

Calls

4 calls:

7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
7.0ms	(/ 1 (+ alpha (+ beta 2.0)))
12.0ms	(* beta (/ 1 (+ alpha (+ beta 2.0))))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
5.0ms	(/ 1 (+ alpha (+ beta 2.0)))
6.0ms	(* beta (/ 1 (+ alpha (+ beta 2.0))))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5332	1448

prune180.0ms

Filtered

87 candidates to 148 candidates (-70.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	148	8	156

Merged error: 3.4b

Counts

156 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`exp-prod` `distribute-lft-out`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `associate-/r*`
4×	`log-prod`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `exp-sum` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 88

Calls

4 calls:

13.0ms	(exp (- (/ alpha (+ alpha (+ beta 2.0))) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ alpha (+ beta 2.0))) 1.0)
13.0ms	(log (exp (- (/ alpha (+ alpha (+ beta 2.0))) 1.0)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(exp (- (/ alpha (+ alpha (+ beta 2.0))) 1.0))
9.0ms	(/ beta (+ (+ alpha beta) 2.0))
11.0ms	(- (/ alpha (+ alpha (+ beta 2.0))) 1.0)
12.0ms	(log (exp (- (/ alpha (+ alpha (+ beta 2.0))) 1.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4942	1131
1	4942	1131

prune150.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	100	8	108

Merged error: 3.4b

Counts

108 → 8

regimes129.0ms

Accuracy

77% (2.9b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 16.0b

bsearch11.0ms

Steps

Iters	Range		Point
6	7729150.201438462	71105696.91140532	64890976.75085129

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	262	50
1	262	50

end0.0ms

sample744.0ms

Algorithm

intervals

Results

193.0ms	5792×	body	80	valid
138.0ms	859×	body	1280	valid
134.0ms	8000×	pre	80	true
90.0ms	724×	body	640	valid
40.0ms	420×	body	320	valid
13.0ms	205×	body	160	valid

Details

analyze3.0ms

sample25.0ms

simplify58.0ms

prune5.0ms

localize9.0ms

rewrite34.0ms

series19.0ms

simplify51.0ms

prune129.0ms

localize15.0ms

rewrite55.0ms

series41.0ms

simplify50.0ms

prune202.0ms

localize14.0ms

rewrite45.0ms

series29.0ms

simplify61.0ms

prune180.0ms

localize19.0ms

rewrite47.0ms

series42.0ms

simplify73.0ms

prune150.0ms

regimes129.0ms

bsearch11.0ms

simplify4.0ms

end0.0ms

sample744.0ms

Profiling