Details

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.280762%

Guaranteed chance to sample good point: 62.857376%

Results

9.0ms	33×	body	2560	valid
8.0ms	161×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	27×	body	640	valid
1.0ms	21×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	10×	body	80	invalid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify362.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	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: 33.6b

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))
0.6b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify138.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune148.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	81	11	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 5.3b

Counts

93 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
4.0b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.3b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `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 → 200

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
47.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	708	3365
1	3231	3197
2	5001	3171

prune229.0ms

Filtered

142 candidates to 212 candidates (-49.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	214	9	223

Merged error: 5.2b

Counts

223 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (/ (* (/ a (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
20.3b	(sqrt (- (* b_2 b_2) (* a c)))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
36×	`add-cube-cbrt`
29×	`add-exp-log`
28×	`cbrt-prod`
20×	`add-cbrt-cube`
16×	`associate-/l*`
15×	`cbrt-undiv` `div-exp`
13×	`sqrt-prod`
8×	`cbrt-div` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
7×	`pow1` `flip3--` `flip--`
6×	`sqrt-div`
5×	`div-inv`
4×	`distribute-rgt-neg-in` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r*`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 135

Calls

4 calls:

35.0ms	(/ (/ (* (/ a (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (/ (* (/ a (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify89.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	696	3504
1	3228	3280
2	5002	3262

prune159.0ms

Filtered

111 candidates to 147 candidates (-32.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	147	9	156

Merged error: 5.2b

Counts

156 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.4b	(- (* b_2 b_2) (* a c))
15.8b	(/ (* a c) (* a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity`
5×	`pow1` `add-cube-cbrt`
4×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `sqrt-prod` `flip--` `cbrt-unprod`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 68

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ (* a c) (* a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(/ (* a c) (* a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	389	714
1	1961	576
2	5002	565

prune76.0ms

Filtered

57 candidates to 80 candidates (-40.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	81	8	89

Merged error: 5.2b

Counts

89 → 8

regimes249.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.3b

bsearch116.0ms

Steps

Iters	Range	Point
8	9.608890786502778e+149	4.3356485419085283e+154	1.1830319413214954e+150
9	-8.902695874747848e-234	-8.087944061124773e-243	-1.3677778830552216e-242
10	-3.9962543486986324e+65	-2.175728114863298e+54	-3.9577108661634927e+65

Iters

Range

Point

9.608890786502778e+149

4.3356485419085283e+154

1.1830319413214954e+150

-8.902695874747848e-234

-8.087944061124773e-243

-1.3677778830552216e-242

-3.9962543486986324e+65

-2.175728114863298e+54

-3.9577108661634927e+65

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	24
1	44	24

end0.0ms

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.280762%

Guaranteed chance to sample good point: 62.857376%

Results

266.0ms	1055×	body	2560	valid
240.0ms	5161×	body	80	valid
176.0ms	853×	body	1280	valid
81.0ms	488×	body	640	valid
35.0ms	117×	body	5120	valid
26.0ms	212×	body	320	valid
22.0ms	506×	body	80	nan
14.0ms	114×	body	160	valid
8.0ms	175×	body	80	invalid

Details

sample2.0s

simplify362.0ms

prune5.0ms

localize11.0ms

rewrite48.0ms

series62.0ms

simplify138.0ms

prune148.0ms

localize11.0ms

rewrite45.0ms

series107.0ms

simplify104.0ms

prune229.0ms

localize16.0ms

rewrite54.0ms

series88.0ms

simplify89.0ms

prune159.0ms

localize11.0ms

rewrite30.0ms

series72.0ms

simplify53.0ms

prune76.0ms

regimes249.0ms

bsearch116.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling