Details

analyze509.0ms

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

sample47.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
2.0ms	20×	body	80	nan
1.0ms	8×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	68	38
1	68	38

prune13.0ms

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

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(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))
15.0ms	(- (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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4970	985
1	4970	985

prune174.0ms

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: 4.4b

Counts

72 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.9b	(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:

5.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series51.0ms

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

simplify70.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4930	985
1	4930	985

prune144.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Merged error: 4.4b

Counts

76 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

8.5b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

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

series57.0ms

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

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4960	941
1	4960	941

prune187.0ms

Filtered

60 candidates to 70 candidates (-16.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	70	6	76

Merged error: 4.4b

Counts

76 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.9b	(/ (- (neg b) (- b (* 2.0 (* c (/ a b))))) (* 2.0 a))
3.3b	(* c (/ a b))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`times-frac`
15×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-r`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
4×	`distribute-lft-out--`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-l` `prod-exp` `sqrt-prod` `flip--` `cbrt-unprod`
2×	`distribute-rgt-neg-in` `sqrt-div` `div-inv` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative`

Counts

4 → 88

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (- (neg b) (- b (* 2.0 (* c (/ a b))))) (* 2.0 a))
7.0ms	(* c (/ a b))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (- (neg b) (- b (* 2.0 (* c (/ a b))))) (* 2.0 a))
5.0ms	(* c (/ a b))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify37.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5243	1251

prune155.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	97	9	106

Merged error: 4.4b

Counts

106 → 9

regimes287.0ms

Accuracy

92.2% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 20.1b

bsearch535.0ms

Steps

Iters	Range		Point
10	4.6945955040955335e+35	1.0029455004911476e+51	9.662367023935268e+49
4	-6.980730338093689e+143	-3.4992013104774966e+143	-3.681287876338451e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	122
1	60	122

end0.0ms

analyze494.0ms

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

sample1.0s

Algorithm

intervals

Results

713.0ms	8000×	body	80	valid
61.0ms	688×	body	80	nan
34.0ms	386×	body	80	invalid

Details

analyze509.0ms

sample47.0ms

simplify3.0ms

prune13.0ms

localize25.0ms

rewrite19.0ms

series52.0ms

simplify50.0ms

prune174.0ms

localize21.0ms

rewrite22.0ms

series51.0ms

simplify70.0ms

prune144.0ms

localize29.0ms

rewrite18.0ms

series57.0ms

simplify37.0ms

prune187.0ms

localize24.0ms

rewrite27.0ms

series38.0ms

simplify37.0ms

prune155.0ms

regimes287.0ms

bsearch535.0ms

simplify2.0ms

end0.0ms

analyze494.0ms

sample1.0s

Profiling