Details

analyze589.0ms

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

sample42.0ms

Algorithm

intervals

Results

8.0ms	32×	body	2560	valid
8.0ms	33×	body	1280	valid
7.0ms	157×	body	80	valid
2.0ms	6×	body	5120	valid
2.0ms	11×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	16×	body	80	nan
0.0ms	4×	body	160	valid
0.0ms	7×	body	80	invalid

simplify475.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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: 33.8b

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)
0.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

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:

10.0ms	(/ (- (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)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune135.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 3.9b

Counts

102 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.8b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.7b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`sqrt-prod` `associate-/r/`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `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 → 126

Calls

4 calls:

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

series121.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5022	2592

prune141.0ms

Filtered

105 candidates to 138 candidates (-31.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	139	7	146

Merged error: 3.8b

Counts

146 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

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:

10.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ c (- (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))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4871	1374
1	4871	1374

prune104.0ms

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	0	6	6
Picked	0	1	1
Done	0	0	0
Total	92	8	100

Merged error: 3.8b

Counts

100 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.7b	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
2.8b	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`associate-r`
22×	`times-frac`
18×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
8×	`difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `associate-l` `associate-/r*` `flip--`
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 → 96

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
12.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
55.0ms	(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
40.0ms	(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4915	1484
1	4915	1484

prune86.0ms

Filtered

79 candidates to 108 candidates (-36.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Merged error: 3.8b

Counts

116 → 8

regimes232.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.9b

bsearch77.0ms

Steps

Iters	Range		Point
8	5.0643450867435756e+98	2.188055895981057e+101	1.1151986711123477e+101
9	3.442968035548936e-179	9.033465428006664e-174	8.199750137875297e-179
7	-2.398989886538497e+89	-2.4786792112297897e+87	-6.97094297046047e+88

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	55
1	89	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

274.0ms	1072×	body	2560	valid
220.0ms	5129×	body	80	valid
188.0ms	924×	body	1280	valid
71.0ms	449×	body	640	valid
35.0ms	117×	body	5120	valid
33.0ms	769×	body	80	nan
29.0ms	225×	body	320	valid
10.0ms	240×	body	80	invalid
7.0ms	84×	body	160	valid

Details

analyze589.0ms

sample42.0ms

simplify475.0ms

prune5.0ms

localize11.0ms

rewrite32.0ms

series66.0ms

simplify63.0ms

prune135.0ms

localize9.0ms

rewrite40.0ms

series121.0ms

simplify51.0ms

prune141.0ms

localize10.0ms

rewrite27.0ms

series82.0ms

simplify63.0ms

prune104.0ms

localize11.0ms

rewrite40.0ms

series122.0ms

simplify55.0ms

prune86.0ms

regimes232.0ms

bsearch77.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling