Details

analyze505.0ms

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample39.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	20×	body	80	nan
1.0ms	13×	body	80	invalid

simplify222.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (221.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 18.6b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (neg b) (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)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4901	985
1	4901	985

prune176.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Merged error: 5.9b

Counts

72 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 58

Calls

4 calls:

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

series52.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (neg b) (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))))

simplify54.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4997	985
1	4997	985

prune158.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 5.9b

Counts

76 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

10.8b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 59

Calls

4 calls:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4873	981
1	4873	981

prune205.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	70	8	78

Merged error: 5.9b

Counts

78 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

20.8b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 58

Calls

4 calls:

5.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))))
6.0ms	(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:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5116	953

prune198.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	70	8	78

Merged error: 5.9b

Counts

78 → 8

regimes310.0ms

Accuracy

92.7% (1.1b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 20.1b

bsearch63.0ms

Steps

Iters	Range		Point
8	2.0845070635952363e+63	3.092620751314997e+66	2.918713991694268e+66
10	-9.714022645000374e+140	-6.757142358012758e+129	-4.7481148527399205e+135

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	187	129
1	187	129

end0.0ms

sample998.0ms

Algorithm

intervals

Results

702.0ms	8000×	body	80	valid
57.0ms	705×	body	80	nan
34.0ms	418×	body	80	invalid

Details

analyze505.0ms

sample39.0ms

simplify222.0ms

prune12.0ms

localize21.0ms

rewrite22.0ms

series53.0ms

simplify52.0ms

prune176.0ms

localize21.0ms

rewrite22.0ms

series52.0ms

simplify54.0ms

prune158.0ms

localize27.0ms

rewrite17.0ms

series58.0ms

simplify47.0ms

prune205.0ms

localize35.0ms

rewrite21.0ms

series57.0ms

simplify47.0ms

prune198.0ms

regimes310.0ms

bsearch63.0ms

simplify3.0ms

end0.0ms

sample998.0ms

Profiling