Details

analyze457.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample42.0ms

Algorithm

intervals

Results

9.0ms	32×	body	2560	valid
8.0ms	159×	body	80	valid
8.0ms	33×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	21×	body	80	nan
1.0ms	10×	body	80	invalid
0.0ms	5×	body	160	valid

simplify201.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (200.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5340	1316

prune162.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 5.9b

Counts

83 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`add-exp-log`
22×	`add-cube-cbrt` `associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 105

Calls

4 calls:

18.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
5.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4968	1950
1	4968	1950

prune177.0ms

Filtered

82 candidates to 117 candidates (-42.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	116	11	127

Merged error: 5.8b

Counts

127 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4973	975
1	4973	975

prune229.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	70	12	82

Merged error: 5.8b

Counts

82 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.5b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.5b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4912	936
1	4912	936

prune236.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	68	12	80

Merged error: 5.8b

Counts

80 → 12

regimes400.0ms

Accuracy

84.1% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.2b

bsearch57.0ms

Steps

Iters	Range		Point
8	3.136927218490703e-38	6.7717606835572935e-34	4.262847488835461e-38
9	-2.1384945482719905e+81	-1.7202665995895133e+72	-1.623300591180788e+76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	98	42
1	98	42

end0.0ms

sample1.2s

Algorithm

intervals

Results

315.0ms	1056×	body	2560	valid
270.0ms	5145×	body	80	valid
223.0ms	899×	body	1280	valid
91.0ms	473×	body	640	valid
35.0ms	97×	body	5120	valid
34.0ms	688×	body	80	nan
29.0ms	208×	body	320	valid
20.0ms	385×	body	80	invalid
12.0ms	122×	body	160	valid

Details

analyze457.0ms

sample42.0ms

simplify201.0ms

prune8.0ms

localize14.0ms

rewrite28.0ms

series66.0ms

simplify41.0ms

prune162.0ms

localize12.0ms

rewrite37.0ms

series74.0ms

simplify54.0ms

prune177.0ms

localize16.0ms

rewrite21.0ms

series59.0ms

simplify40.0ms

prune229.0ms

localize29.0ms

rewrite18.0ms

series79.0ms

simplify53.0ms

prune236.0ms

regimes400.0ms

bsearch57.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling