Details

analyze2.0ms

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	190×	body	80	valid
4.0ms	28×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	7×	body	160	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

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: 15.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- 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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series18.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5370	1005

prune123.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

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: 14.9b

Counts

72 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
1.8b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite56.0ms

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

series34.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6016	1670

prune187.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	124	8	132

Merged error: 2.5b

Counts

132 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha (+ beta 2.0)) beta)
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.3b	(/ 1 (/ (+ alpha (+ beta 2.0)) beta))
1.8b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite47.0ms

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 → 188

Calls

4 calls:

9.0ms	(/ (+ alpha (+ beta 2.0)) beta)
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
10.0ms	(/ 1 (/ (+ alpha (+ beta 2.0)) beta))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series28.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (+ alpha (+ beta 2.0)) beta)
6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
7.0ms	(/ 1 (/ (+ alpha (+ beta 2.0)) beta))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4960	2464
1	4960	2464

prune227.0ms

Filtered

113 candidates to 200 candidates (-77.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	200	8	208

Merged error: 2.5b

Counts

208 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ alpha (+ beta 2.0)))
1.8b	(- (/ alpha (+ alpha (+ beta 2.0))) 1.0)
1.8b	(log (exp (- (/ alpha (+ alpha (+ beta 2.0))) 1.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(/ alpha (+ alpha (+ beta 2.0)))
13.0ms	(- (/ alpha (+ alpha (+ beta 2.0))) 1.0)
11.0ms	(log (exp (- (/ alpha (+ alpha (+ beta 2.0))) 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5048	1340

prune167.0ms

Filtered

84 candidates to 120 candidates (-42.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	120	8	128

Merged error: 2.5b

Counts

128 → 8

regimes132.0ms

Accuracy

72.8% (3.3b remaining)

Error of 6.1b against oracle of 2.8b and baseline of 15.0b

bsearch52.0ms

Steps

Iters	Range		Point
7	1.0963309411456621e+140	1.64792997264692e+142	1.1231273814540445e+140
8	4.2138310674814273e+117	9.599902580703627e+121	9.366035363736922e+121
5	808849356432405.5	2889541528938098.5	825090542879979.5

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	373	80
1	373	80

end0.0ms

sample700.0ms

Algorithm

intervals

Results

186.0ms	5942×	body	80	valid
128.0ms	821×	body	1280	valid
126.0ms	8000×	pre	80	true
82.0ms	696×	body	640	valid
34.0ms	356×	body	320	valid
12.0ms	185×	body	160	valid

Details

analyze2.0ms

sample25.0ms

simplify56.0ms

prune5.0ms

localize8.0ms

rewrite34.0ms

series18.0ms

simplify46.0ms

prune123.0ms

localize11.0ms

rewrite56.0ms

series34.0ms

simplify44.0ms

prune187.0ms

localize13.0ms

rewrite47.0ms

series28.0ms

simplify70.0ms

prune227.0ms

localize15.0ms

rewrite43.0ms

series36.0ms

simplify42.0ms

prune167.0ms

regimes132.0ms

bsearch52.0ms

simplify8.0ms

end0.0ms

sample700.0ms

Profiling