Details

sample829.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 20.645142%

Guaranteed chance to sample good point: 86.566935%

Results

9.0ms	32×	body	2560	valid
8.0ms	182×	body	80	valid
7.0ms	31×	body	1280	valid
3.0ms	19×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	14×	body	80	nan
0.0ms	1×	body	160	valid

simplify366.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

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: 35.0b

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)
0.2b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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 → 91

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (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))
37.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune152.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 4.9b

Counts

104 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
4.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
54.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune234.0ms

Filtered

144 candidates to 196 candidates (-36.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	198	9	207

Merged error: 4.8b

Counts

207 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
2.6b	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
4.4b	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

3063×	`times-frac`
1685×	`add-sqr-sqrt`
1444×	`*-un-lft-identity`
1204×	`add-cube-cbrt`
240×	`difference-of-squares`
237×	`associate-/l*`
123×	`sqrt-prod`
120×	`distribute-lft-out--`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1022

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
53.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
23.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify248.0ms

Algorithm

egg-herbie

Counts

1034 → 1034

Iterations

Useful iterations: 1 (71.0ms)

Iter	Nodes	Cost
0	4207	20994
1	5001	20405

prune940.0ms

Filtered

572 candidates to 1034 candidates (-80.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	1033	1	1034
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	1033	10	1043

Merged error: 4.8b

Counts

1043 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
14.5b	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
101×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
76×	`associate-r`
60×	`add-cube-cbrt`
39×	`add-exp-log`
25×	`add-cbrt-cube`
20×	`difference-of-squares`
15×	`prod-exp`
13×	`sqrt-prod`
12×	`div-exp`
10×	`pow1` `distribute-lft-out--`
9×	`cbrt-unprod`
8×	`add-log-exp`
6×	`cbrt-undiv` `flip3--` `associate-/r/` `flip--`
4×	`div-inv`
3×	`pow-prod-down`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `-commutative`

Counts

4 → 146

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	895	1587
1	4994	1371
2	5001	1371

prune137.0ms

Filtered

103 candidates to 158 candidates (-53.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	158	10	168

Merged error: 4.8b

Counts

168 → 10

regimes443.0ms

Accuracy

89% (3.0b remaining)

Error of 8.7b against oracle of 5.7b and baseline of 32.7b

bsearch82.0ms

Steps

Iters	Range	Point
11	1.4124388747746146e+74	4.780152256637718e+102	1.9796318503870474e+101
10	-2.1226190201697567e-246	-4.0041773931369285e-258	-9.653169828473534e-258
3	-4.072722608680232e-37	-3.304864140519196e-37	-3.99618659303816e-37

Iters

Range

Point

1.4124388747746146e+74

4.780152256637718e+102

1.9796318503870474e+101

-2.1226190201697567e-246

-4.0041773931369285e-258

-9.653169828473534e-258

-4.072722608680232e-37

-3.304864140519196e-37

-3.99618659303816e-37

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 20.645142%

Guaranteed chance to sample good point: 86.566935%

Results

286.0ms	1121×	body	2560	valid
269.0ms	5868×	body	80	valid
187.0ms	881×	body	1280	valid
78.0ms	456×	body	640	valid
31.0ms	102×	body	5120	valid
28.0ms	222×	body	320	valid
23.0ms	537×	body	80	nan
9.0ms	112×	body	160	valid

Details

sample829.0ms

simplify366.0ms

prune5.0ms

localize11.0ms

rewrite31.0ms

series75.0ms

simplify41.0ms

prune152.0ms

localize10.0ms

rewrite41.0ms

series119.0ms

simplify104.0ms

prune234.0ms

localize12.0ms

rewrite193.0ms

series70.0ms

simplify248.0ms

prune940.0ms

localize10.0ms

rewrite45.0ms

series75.0ms

simplify111.0ms

prune137.0ms

regimes443.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling