Details

analyze493.0ms

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

sample35.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
2.0ms	20×	body	80	nan
1.0ms	13×	body	80	invalid

simplify215.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (213.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

prune15.0ms

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: 18.9b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* 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)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify54.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4900	1063
1	4900	1063

prune184.0ms

Filtered

63 candidates to 74 candidates (-17.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 5.9b

Counts

76 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
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))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4895	1082
1	4895	1082

prune166.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Merged error: 5.9b

Counts

80 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

14.2b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4873	981
1	4873	981

prune205.0ms

Filtered

60 candidates to 71 candidates (-18.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 5.9b

Counts

78 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5034	1039

prune194.0ms

Filtered

62 candidates to 74 candidates (-19.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	73	9	82

Merged error: 5.9b

Counts

82 → 9

regimes302.0ms

Accuracy

84.8% (2.1b remaining)

Error of 7.8b against oracle of 5.7b and baseline of 19.6b

bsearch61.0ms

Steps

Iters	Range		Point
9	2.4869401527017716e-36	1.6972718612280455e-29	1.669301981767778e-29
8	-5.446691712832163e+139	-7.507788368454394e+136	-3.1989072191100113e+139

simplify17.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	784	129
1	784	129

end0.0ms

sample973.0ms

Algorithm

intervals

Results

692.0ms	8000×	body	80	valid
54.0ms	655×	body	80	nan
35.0ms	422×	body	80	invalid

Details

analyze493.0ms

sample35.0ms

simplify215.0ms

prune15.0ms

localize21.0ms

rewrite27.0ms

series60.0ms

simplify54.0ms

prune184.0ms

localize21.0ms

rewrite26.0ms

series60.0ms

simplify72.0ms

prune166.0ms

localize30.0ms

rewrite18.0ms

series57.0ms

simplify50.0ms

prune205.0ms

localize31.0ms

rewrite23.0ms

series60.0ms

simplify51.0ms

prune194.0ms

regimes302.0ms

bsearch61.0ms

simplify17.0ms

end0.0ms

sample973.0ms

Profiling