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

sample47.0ms

Algorithm

intervals

Results

14.0ms	40×	body	2560	valid
9.0ms	162×	body	80	valid
7.0ms	28×	body	1280	valid
2.0ms	13×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	15×	body	80	invalid
1.0ms	15×	body	80	nan
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify211.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (209.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune7.0ms

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: 32.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5946	1448

prune156.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 4.4b

Counts

88 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.0b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
14.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
45.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
61.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5232	2497

prune188.0ms

Filtered

84 candidates to 124 candidates (-47.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	122	10	132

Merged error: 4.3b

Counts

132 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

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:

12.0ms	(/ c (- (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))))

series88.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
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))))

simplify63.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune152.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	6	8
Picked	1	0	1
Done	1	0	1
Total	94	9	103

Merged error: 4.3b

Counts

103 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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×	`add-exp-log` `sqrt-prod` `add-log-exp`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `div-inv` `inv-pow`

Counts

4 → 85

Calls

4 calls:

10.0ms	(/ 1 (- (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))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4954	1625
1	4954	1625

prune120.0ms

Filtered

64 candidates to 97 candidates (-51.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 4.3b

Counts

106 → 10

regimes286.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.5b

bsearch104.0ms

Steps

Iters	Range		Point
9	5.504342935150587e+91	1.3598499897243303e+101	2.2238939560125314e+96
9	-6.93148006526933e-304	9.06754721703624e-307	1.382893771623077e-308
9	-8.50812147612246e+156	-3.2673394609279968e+150	-4.415709553812456e+150

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	174	60
1	174	60

end0.0ms

sample1.3s

Algorithm

intervals

Results

326.0ms	1067×	body	2560	valid
270.0ms	5148×	body	80	valid
229.0ms	909×	body	1280	valid
87.0ms	454×	body	640	valid
37.0ms	103×	body	5120	valid
32.0ms	661×	body	80	nan
31.0ms	203×	body	320	valid
20.0ms	386×	body	80	invalid
11.0ms	116×	body	160	valid

Details

analyze457.0ms

sample47.0ms

simplify211.0ms

prune7.0ms

localize11.0ms

rewrite30.0ms

series61.0ms

simplify43.0ms

prune156.0ms

localize12.0ms

rewrite44.0ms

series135.0ms

simplify41.0ms

prune188.0ms

localize13.0ms

rewrite30.0ms

series88.0ms

simplify63.0ms

prune152.0ms

localize14.0ms

rewrite28.0ms

series59.0ms

simplify37.0ms

prune120.0ms

regimes286.0ms

bsearch104.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling