Details

analyze465.0ms

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

sample44.0ms

Algorithm

intervals

Results

9.0ms	159×	body	80	valid
8.0ms	26×	body	2560	valid
7.0ms	30×	body	1280	valid
5.0ms	27×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	19×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	11×	body	80	invalid
0.0ms	5×	body	160	valid

simplify200.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (199.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune9.0ms

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: 34.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.4b	(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:

12.0ms	(/ (- (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))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (- (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)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5083	1316

prune183.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 3.1b

Counts

83 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

14.0ms	(* a (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
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))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* a (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5026	1451

prune188.0ms

Filtered

70 candidates to 95 candidates (-35.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	94	11	105

Merged error: 3.1b

Counts

105 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms

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))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4893	975
1	4893	975

prune234.0ms

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: 3.1b

Counts

82 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.1b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.1b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

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:

14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
26.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5730	940

prune238.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	67	13	80

Merged error: 3.1b

Counts

80 → 13

regimes433.0ms

Accuracy

84.2% (4.4b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 33.3b

bsearch48.0ms

Steps

Iters	Range		Point
7	1.1340168675459213e-64	3.1363185241140265e-63	1.5308604502336437e-63
7	-6.569266512535093e+93	-4.037383248473519e+91	-5.254235259318601e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	167	38
1	167	38

end0.0ms

sample1.3s

Algorithm

intervals

Results

312.0ms	1028×	body	2560	valid
283.0ms	5181×	body	80	valid
223.0ms	881×	body	1280	valid
94.0ms	473×	body	640	valid
38.0ms	105×	body	5120	valid
37.0ms	671×	body	80	nan
32.0ms	219×	body	320	valid
23.0ms	438×	body	80	invalid
11.0ms	113×	body	160	valid

Details

analyze465.0ms

sample44.0ms

simplify200.0ms

prune9.0ms

localize10.0ms

rewrite28.0ms

series61.0ms

simplify41.0ms

prune183.0ms

localize12.0ms

rewrite31.0ms

series89.0ms

simplify45.0ms

prune188.0ms

localize16.0ms

rewrite20.0ms

series57.0ms

simplify58.0ms

prune234.0ms

localize23.0ms

rewrite17.0ms

series79.0ms

simplify58.0ms

prune238.0ms

regimes433.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling