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

sample64.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify219.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (217.0ms)

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: 20.3b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

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:

9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(+ (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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4900	1063
1	4900	1063

prune189.0ms

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: 4.9b

Counts

76 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.4b	(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:

9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (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))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4895	1082
1	4895	1082

prune160.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

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

Merged error: 4.9b

Counts

80 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

12.4b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.4b	(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)))

series59.0ms

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)))))))
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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4873	981
1	4873	981

prune193.0ms

Filtered

60 candidates to 71 candidates (-18.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	71	7	78

Merged error: 4.9b

Counts

78 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

11.7b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* 4.0 (* a c))))
24.2b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

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

series98.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
26.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4903	1193
1	4903	1193

prune176.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	66	7	73

Merged error: 4.9b

Counts

73 → 7

regimes271.0ms

Accuracy

91.6% (1.2b remaining)

Error of 7.1b against oracle of 5.9b and baseline of 20.2b

bsearch90.0ms

Steps

Iters	Range		Point
10	4.188433678503961e+46	6.0316351026260574e+57	5.9747984435476024e+57
9	-1.0912392884303037e+142	-2.907909039459474e+136	-5.790101578899714e+138

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	177	116
1	177	116

end0.0ms

sample1.8s

Algorithm

intervals

Results

654.0ms

8000×

body

valid

Details

analyze505.0ms

sample64.0ms

simplify219.0ms

prune12.0ms

localize21.0ms

rewrite29.0ms

series58.0ms

simplify57.0ms

prune189.0ms

localize24.0ms

rewrite26.0ms

series60.0ms

simplify72.0ms

prune160.0ms

localize28.0ms

rewrite18.0ms

series59.0ms

simplify48.0ms

prune193.0ms

localize29.0ms

rewrite18.0ms

series98.0ms

simplify69.0ms

prune176.0ms

regimes271.0ms

bsearch90.0ms

simplify3.0ms

end0.0ms

sample1.8s

Profiling