Details

analyze599.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample41.0ms

Algorithm

intervals

Results

9.0ms	34×	body	2560	valid
7.0ms	164×	body	80	valid
6.0ms	30×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	20×	body	80	nan
1.0ms	2×	body	5120	valid
0.0ms	9×	body	80	invalid
0.0ms	3×	body	160	valid

simplify439.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

prune5.0ms

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: 33.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.3b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

Calls

4 calls:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5018	1301

prune135.0ms

Filtered

69 candidates to 91 candidates (-31.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	10	92

Merged error: 5.3b

Counts

92 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.1b	(/ (/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.1b	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(/ (/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.0ms	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(/ (/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4939	2825
1	4939	2825

prune142.0ms

Filtered

105 candidates to 147 candidates (-40.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	4	4	8
Picked	0	1	1
Done	1	0	1
Total	149	8	157

Merged error: 5.1b

Counts

157 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

9.0ms	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4952	1531
1	4952	1531

prune110.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	98	10	108

Merged error: 5.1b

Counts

108 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

10.1b	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

11.0ms	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5622	1140

prune96.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	88	10	98

Merged error: 5.1b

Counts

98 → 10

regimes296.0ms

Accuracy

93.6% (1.5b remaining)

Error of 6.9b against oracle of 5.3b and baseline of 29.5b

bsearch741.0ms

Steps

Iters	Range	Point
9	1.9386637509025113e+44	7.182658398204528e+53	7.063724985986483e+53
10	-5.266358150841853e-302	2.0788719851752353e-304	-2.09305734344904e-310
10	-2.5578186049563775e+160	-9.22491112247463e+143	-1.4636905970896212e+146

Iters

Range

Point

1.9386637509025113e+44

7.182658398204528e+53

7.063724985986483e+53

-5.266358150841853e-302

2.0788719851752353e-304

-2.09305734344904e-310

-2.5578186049563775e+160

-9.22491112247463e+143

-1.4636905970896212e+146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	58
1	42	58

end0.0ms

analyze397.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample1.1s

Algorithm

intervals

Results

271.0ms	1086×	body	2560	valid
222.0ms	5106×	body	80	valid
181.0ms	879×	body	1280	valid
76.0ms	455×	body	640	valid
40.0ms	122×	body	5120	valid
32.0ms	771×	body	80	nan
28.0ms	237×	body	320	valid
11.0ms	236×	body	80	invalid
9.0ms	115×	body	160	valid

Details

analyze599.0ms

sample41.0ms

simplify439.0ms

prune5.0ms

localize12.0ms

rewrite29.0ms

series71.0ms

simplify44.0ms

prune135.0ms

localize10.0ms

rewrite42.0ms

series116.0ms

simplify65.0ms

prune142.0ms

localize10.0ms

rewrite26.0ms

series81.0ms

simplify70.0ms

prune110.0ms

localize21.0ms

rewrite24.0ms

series87.0ms

simplify43.0ms

prune96.0ms

regimes296.0ms

bsearch741.0ms

simplify2.0ms

end0.0ms

analyze397.0ms

sample1.1s

Profiling