Details

analyze459.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample47.0ms

Algorithm

intervals

Results

13.0ms	42×	body	2560	valid
11.0ms	164×	body	80	valid
6.0ms	24×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	24×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	17×	body	80	invalid
0.0ms	2×	body	160	valid

simplify181.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (179.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune8.0ms

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: 33.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.7b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
22.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 69

Calls

4 calls:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5899	1226

prune155.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	7	82

Merged error: 5.4b

Counts

82 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) 3.0)
0.7b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
0.8b	(- (* b b) (* 3.0 (* a c)))
22.4b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) 3.0)
7.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
6.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) 3.0)
14.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
8.0ms	(- (* b b) (* 3.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5647	1641

prune148.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Merged error: 5.4b

Counts

101 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 3.0 (- (sqrt (- (* b b) (* 3.0 (* a c)))) b))
0.7b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
0.8b	(- (* b b) (* 3.0 (* a c)))
22.4b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/ 3.0 (- (sqrt (- (* b b) (* 3.0 (* a c)))) b))
9.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 3.0 (- (sqrt (- (* b b) (* 3.0 (* a c)))) b))
15.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
8.0ms	(- (* b b) (* 3.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5258	1618

prune149.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	93	9	102

Merged error: 5.3b

Counts

102 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 3.0 (* a c)))
22.4b	(sqrt (- (* b b) (* 3.0 (* a c))))
22.4b	(sqrt (- (* b b) (* 3.0 (* a c))))
22.4b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 56

Calls

4 calls:

4.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))
6.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify36.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5246	878

prune180.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	67	10	77

Merged error: 5.3b

Counts

77 → 10

regimes598.0ms

Accuracy

83% (4.9b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 34.3b

bsearch60.0ms

Steps

Iters	Range		Point
9	4.400864185653009e-22	7.041687525152563e-14	5.20071916789479e-20
9	-4.402975412786172e+159	-1.5515592463417882e+150	-3.178178917587814e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	40
1	106	40

end0.0ms

sample1.3s

Algorithm

intervals

Results

346.0ms	1095×	body	2560	valid
276.0ms	5088×	body	80	valid
239.0ms	933×	body	1280	valid
90.0ms	443×	body	640	valid
44.0ms	116×	body	5120	valid
36.0ms	665×	body	80	nan
33.0ms	202×	body	320	valid
19.0ms	364×	body	80	invalid
12.0ms	123×	body	160	valid

Details

analyze459.0ms

sample47.0ms

simplify181.0ms

prune8.0ms

localize11.0ms

rewrite29.0ms

series64.0ms

simplify42.0ms

prune155.0ms

localize11.0ms

rewrite29.0ms

series53.0ms

simplify57.0ms

prune148.0ms

localize12.0ms

rewrite29.0ms

series57.0ms

simplify56.0ms

prune149.0ms

localize16.0ms

rewrite19.0ms

series50.0ms

simplify36.0ms

prune180.0ms

regimes598.0ms

bsearch60.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling