Details

analyze457.0ms

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

sample42.0ms

Algorithm

intervals

Results

11.0ms	38×	body	2560	valid
8.0ms	163×	body	80	valid
7.0ms	29×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid
0.0ms	7×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

prune6.0ms

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: 33.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

13.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5092	1264

prune154.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	9	82

Merged error: 5.6b

Counts

82 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
4.4b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.0b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`sqrt-prod`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`distribute-rgt-neg-in` `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 → 113

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
42.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
58.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5074	2452

prune171.0ms

Filtered

79 candidates to 125 candidates (-58.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	127	7	134

Merged error: 5.5b

Counts

134 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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

series84.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4942	1771
1	4942	1771

prune141.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	99	8	107

Merged error: 5.5b

Counts

107 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(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)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4932	967
1	4932	967

prune188.0ms

Filtered

62 candidates to 72 candidates (-16.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	72	8	80

Merged error: 5.4b

Counts

80 → 8

regimes355.0ms

Accuracy

93.1% (1.6b remaining)

Error of 7.5b against oracle of 5.8b and baseline of 29.7b

bsearch724.0ms

Steps

Iters	Range	Point
8	2.707438489355542e+36	6.076937178834989e+40	5.954633135651186e+40
8	-6.1312784994282785e-304	-1.3594521996163033e-306	-5.172713162523186e-305
9	-1.5501229272338467e+79	-2.990850712457184e+73	-1.5226398296836354e+79

Iters

Range

Point

2.707438489355542e+36

6.076937178834989e+40

5.954633135651186e+40

-6.1312784994282785e-304

-1.3594521996163033e-306

-5.172713162523186e-305

-1.5501229272338467e+79

-2.990850712457184e+73

-1.5226398296836354e+79

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	62
1	47	62

end0.0ms

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

sample1.2s

Algorithm

intervals

Results

331.0ms	1095×	body	2560	valid
263.0ms	5058×	body	80	valid
219.0ms	890×	body	1280	valid
90.0ms	475×	body	640	valid
42.0ms	116×	body	5120	valid
35.0ms	235×	body	320	valid
32.0ms	654×	body	80	nan
19.0ms	376×	body	80	invalid
13.0ms	131×	body	160	valid

Details

analyze457.0ms

sample42.0ms

simplify3.0ms

prune6.0ms

localize11.0ms

rewrite29.0ms

series60.0ms

simplify46.0ms

prune154.0ms

localize15.0ms

rewrite39.0ms

series124.0ms

simplify47.0ms

prune171.0ms

localize13.0ms

rewrite27.0ms

series84.0ms

simplify61.0ms

prune141.0ms

localize25.0ms

rewrite19.0ms

series55.0ms

simplify65.0ms

prune188.0ms

regimes355.0ms

bsearch724.0ms

simplify1.0ms

end0.0ms

analyze446.0ms

sample1.2s

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