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

sample44.0ms

Algorithm

intervals

Results

10.0ms	42×	body	2560	valid
7.0ms	161×	body	80	valid
6.0ms	24×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	29×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	6×	body	160	valid
0.0ms	1×	body	5120	valid
0.0ms	5×	body	80	invalid

simplify480.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	713	13
1	713	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: 36.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

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-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 89

Calls

4 calls:

29.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune151.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	90	11	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	11	102

Merged error: 6.6b

Counts

102 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.8b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.4b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
53×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`difference-of-squares`
10×	`associate-/r/`
9×	`associate-/r*` `sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`div-inv` `distribute-lft-out--` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 123

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
60.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4961	2488
1	4961	2488

prune149.0ms

Filtered

102 candidates to 135 candidates (-32.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	137	9	146

Merged error: 6.6b

Counts

146 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 152

Calls

4 calls:

11.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5207	3117

prune150.0ms

Filtered

94 candidates to 164 candidates (-74.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	163	10	173

Merged error: 6.4b

Counts

173 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.9b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.8b	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
14.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
43.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4943	1387
1	4943	1387

prune90.0ms

Filtered

74 candidates to 105 candidates (-41.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	105	10	115

Merged error: 6.4b

Counts

115 → 10

regimes343.0ms

Accuracy

94.9% (1.2b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.7b

bsearch87.0ms

Steps

Iters	Range	Point
8	1.196155847302467e+133	6.923304855903745e+137	7.059358784344947e+133
10	-2.923900964439637e-277	-3.156634362947396e-292	-3.205290969087756e-292
8	-7.438577681810015e+89	-2.443163398651737e+87	-7.356693308942923e+89

Iters

Range

Point

1.196155847302467e+133

6.923304855903745e+137

7.059358784344947e+133

-2.923900964439637e-277

-3.156634362947396e-292

-3.205290969087756e-292

-7.438577681810015e+89

-2.443163398651737e+87

-7.356693308942923e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	57
1	88	57

end0.0ms

sample1.1s

Algorithm

intervals

Results

268.0ms	1097×	body	2560	valid
221.0ms	5113×	body	80	valid
182.0ms	900×	body	1280	valid
68.0ms	425×	body	640	valid
31.0ms	99×	body	5120	valid
31.0ms	761×	body	80	nan
29.0ms	243×	body	320	valid
11.0ms	253×	body	80	invalid
10.0ms	123×	body	160	valid

Details

analyze599.0ms

sample44.0ms

simplify480.0ms

prune5.0ms

localize11.0ms

rewrite51.0ms

series64.0ms

simplify61.0ms

prune151.0ms

localize9.0ms

rewrite36.0ms

series125.0ms

simplify64.0ms

prune149.0ms

localize10.0ms

rewrite37.0ms

series62.0ms

simplify74.0ms

prune150.0ms

localize10.0ms

rewrite41.0ms

series125.0ms

simplify55.0ms

prune90.0ms

regimes343.0ms

bsearch87.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling