Details

analyze446.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample74.0ms

Algorithm

intervals

Results

10.0ms	163×	body	80	valid
9.0ms	28×	body	2560	valid
8.0ms	32×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify208.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (206.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 34.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
14.9b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5946	1448

prune155.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 5.8b

Counts

88 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.6b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

16.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series141.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
64.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5232	2497

prune195.0ms

Filtered

84 candidates to 124 candidates (-47.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	123	9	132

Merged error: 5.7b

Counts

132 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.3b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
53.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune157.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	94	8	102

Merged error: 5.7b

Counts

102 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.5b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (* 1 (/ 2.0 c)) 4.0))
10.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`prod-exp`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1` `div-exp` `associate-r`
6×	`associate-l` `cbrt-unprod`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`cbrt-undiv` `difference-of-squares`
3×	`times-frac`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `1-exp` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (* 1 (/ 2.0 c)) 4.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (* 1 (/ 2.0 c)) 4.0))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5109	1484

prune131.0ms

Filtered

66 candidates to 90 candidates (-36.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	89	9	98

Merged error: 5.7b

Counts

98 → 9

regimes316.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.6b

bsearch121.0ms

Steps

Iters	Range	Point
10	1.3631201305493908e+101	5.717463957312944e+119	2.812515427936131e+118
7	-2.1368779513234288e-302	-1.1225643749268928e-303	-1.1347887231787398e-303
9	-9.6824112406062e+64	-1.677406575753896e+58	-9.103844937062704e+64

Iters

Range

Point

1.3631201305493908e+101

5.717463957312944e+119

2.812515427936131e+118

-2.1368779513234288e-302

-1.1225643749268928e-303

-1.1347887231787398e-303

-9.6824112406062e+64

-1.677406575753896e+58

-9.103844937062704e+64

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	126	63
1	126	63

end0.0ms

sample1.9s

Algorithm

intervals

Results

314.0ms	1089×	body	2560	valid
248.0ms	5116×	body	80	valid
214.0ms	893×	body	1280	valid
89.0ms	468×	body	640	valid
38.0ms	106×	body	5120	valid
34.0ms	225×	body	320	valid
10.0ms	103×	body	160	valid

Details

analyze446.0ms

sample74.0ms

simplify208.0ms

prune7.0ms

localize12.0ms

rewrite30.0ms

series62.0ms

simplify43.0ms

prune155.0ms

localize14.0ms

rewrite43.0ms

series141.0ms

simplify40.0ms

prune195.0ms

localize15.0ms

rewrite30.0ms

series92.0ms

simplify66.0ms

prune157.0ms

localize17.0ms

rewrite33.0ms

series62.0ms

simplify41.0ms

prune131.0ms

regimes316.0ms

bsearch121.0ms

simplify4.0ms

end0.0ms

sample1.9s

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