Details

analyze587.0ms

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

9.0ms	33×	body	2560	valid
7.0ms	170×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	24×	body	80	nan
1.0ms	8×	body	320	valid
0.0ms	10×	body	80	invalid
0.0ms	3×	body	160	valid

simplify484.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

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: 31.7b

Counts

2 → 1

localize12.0ms

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))
1.3b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

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)
4.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune130.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	7	102

Merged error: 4.6b

Counts

102 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.9b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.8b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

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)
13.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (* 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:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(/ (/ (* 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))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5022	2592

prune137.0ms

Filtered

105 candidates to 138 candidates (-31.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	138	7	145

Merged error: 4.5b

Counts

145 → 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))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

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)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (- (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)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4871	1374
1	4871	1374

prune98.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	93	7	100

Merged error: 4.5b

Counts

100 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
1.3b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

17.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
6.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5147	1355

prune89.0ms

Filtered

71 candidates to 99 candidates (-39.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	99	7	106

Merged error: 4.5b

Counts

106 → 7

regimes231.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.2b

bsearch97.0ms

Steps

Iters	Range	Point
8	1.9736146145575333e+149	1.6002854112070645e+152	2.706784727683868e+149
12	1.2031880981201817e-219	1.7641546554469901e-180	1.2144381520308056e-219
9	-7.869574421480348e+160	-7.986216658047056e+155	-8.055509887818825e+155

Iters

Range

Point

1.9736146145575333e+149

1.6002854112070645e+152

2.706784727683868e+149

1.2031880981201817e-219

1.7641546554469901e-180

1.2144381520308056e-219

-7.869574421480348e+160

-7.986216658047056e+155

-8.055509887818825e+155

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	150	56
1	150	56

end0.0ms

sample1.1s

Algorithm

intervals

Results

256.0ms	1033×	body	2560	valid
217.0ms	5079×	body	80	valid
189.0ms	915×	body	1280	valid
78.0ms	495×	body	640	valid
38.0ms	115×	body	5120	valid
31.0ms	784×	body	80	nan
30.0ms	237×	body	320	valid
10.0ms	126×	body	160	valid
9.0ms	227×	body	80	invalid

Details

analyze587.0ms

sample44.0ms

simplify484.0ms

prune5.0ms

localize12.0ms

rewrite35.0ms

series77.0ms

simplify62.0ms

prune130.0ms

localize10.0ms

rewrite41.0ms

series125.0ms

simplify55.0ms

prune137.0ms

localize10.0ms

rewrite28.0ms

series83.0ms

simplify63.0ms

prune98.0ms

localize10.0ms

rewrite38.0ms

series51.0ms

simplify42.0ms

prune89.0ms

regimes231.0ms

bsearch97.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling