Details

analyze601.0ms

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

sample49.0ms

Algorithm

intervals

Results

14.0ms	54×	body	2560	valid
8.0ms	156×	body	80	valid
6.0ms	28×	body	1280	valid
5.0ms	12×	body	640	valid
1.0ms	28×	body	80	nan
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	valid
1.0ms	12×	body	80	invalid

simplify463.0ms

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: 37.3b

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)
0.1b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.2b	(- (* b_2 b_2) (* a c))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune147.0ms

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: 5.8b

Counts

102 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.8b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.1b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.3b	(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)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
58.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5022	2592

prune148.0ms

Filtered

105 candidates to 138 candidates (-31.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Merged error: 5.7b

Counts

146 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

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:

9.0ms	(/ 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)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4871	1374
1	4871	1374

prune111.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	92	10	102

Merged error: 5.7b

Counts

102 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`associate-r`
20×	`times-frac`
16×	`add-cube-cbrt`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`flip3--` `prod-exp` `flip--` `distribute-lft-out--`
3×	`associate-l` `unswap-sqr`
2×	`sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

17.0ms	(* c (/ 1 (- (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)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4940	1230
1	4940	1230

prune94.0ms

Filtered

70 candidates to 99 candidates (-41.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	99	10	109

Merged error: 5.7b

Counts

109 → 10

regimes304.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.1b

bsearch79.0ms

Steps

Iters	Range	Point
6	3.858618465166249e+111	2.873209979156839e+112	9.31225597957106e+111
8	-2.3568830894990782e-272	-8.860538765950511e-277	-8.989497529056973e-277
8	-1.472944944397352e+138	-1.612394586473438e+134	-7.1477916520959866e+134

Iters

Range

Point

3.858618465166249e+111

2.873209979156839e+112

9.31225597957106e+111

-2.3568830894990782e-272

-8.860538765950511e-277

-8.989497529056973e-277

-1.472944944397352e+138

-1.612394586473438e+134

-7.1477916520959866e+134

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	145	54
1	145	54

end0.0ms

sample1.1s

Algorithm

intervals

Results

277.0ms	1092×	body	2560	valid
235.0ms	5144×	body	80	valid
192.0ms	894×	body	1280	valid
67.0ms	416×	body	640	valid
36.0ms	115×	body	5120	valid
34.0ms	804×	body	80	nan
30.0ms	230×	body	320	valid
12.0ms	273×	body	80	invalid
9.0ms	109×	body	160	valid

Details

analyze601.0ms

sample49.0ms

simplify463.0ms

prune5.0ms

localize11.0ms

rewrite44.0ms

series62.0ms

simplify66.0ms

prune147.0ms

localize9.0ms

rewrite40.0ms

series127.0ms

simplify52.0ms

prune148.0ms

localize10.0ms

rewrite26.0ms

series85.0ms

simplify61.0ms

prune111.0ms

localize11.0ms

rewrite35.0ms

series84.0ms

simplify64.0ms

prune94.0ms

regimes304.0ms

bsearch79.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling