Details

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

11.0ms	162×	body	80	valid
8.0ms	32×	body	2560	valid
7.0ms	32×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	13×	body	80	nan
0.0ms	5×	body	160	valid
0.0ms	9×	body	80	invalid

simplify350.0ms

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: 34.1b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
2.0b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (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))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify139.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

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

prune140.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	10	93

Merged error: 6.8b

Counts

93 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.3b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.4b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
14.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
53.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	716	3474
1	3237	3299
2	5002	3273

prune224.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	219	9	228

Merged error: 6.7b

Counts

228 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.7b	(/ (* a c) (* a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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:

4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(/ (* a c) (* a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(/ (* a c) (* a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (42.0ms)

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

prune93.0ms

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: 6.7b

Counts

89 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

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-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 90

Calls

4 calls:

9.0ms	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify38.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	326	944
1	1163	883
2	5001	870

prune86.0ms

Filtered

71 candidates to 102 candidates (-43.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	102	8	110

Merged error: 6.7b

Counts

110 → 8

regimes373.0ms

Accuracy

96% (1.0b remaining)

Error of 6.2b against oracle of 5.2b and baseline of 29.3b

bsearch145.0ms

Steps

Iters	Range	Point
7	4.5708854742457556e+148	1.6394169134044562e+150	4.727151746833199e+148
11	-1.6406029728281883e-258	-4.8778983015564077e-296	-1.0382019606007427e-287
7	-3.440980885963543e+85	-1.3455550657257552e+84	-3.383650589817266e+85

Iters

Range

Point

4.5708854742457556e+148

1.6394169134044562e+150

4.727151746833199e+148

-1.6406029728281883e-258

-4.8778983015564077e-296

-1.0382019606007427e-287

-3.440980885963543e+85

-1.3455550657257552e+84

-3.383650589817266e+85

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	23
1	42	23

end0.0ms

sample2.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

288.0ms	1084×	body	2560	valid
238.0ms	5042×	body	80	valid
201.0ms	954×	body	1280	valid
71.0ms	429×	body	640	valid
42.0ms	134×	body	5120	valid
34.0ms	239×	body	320	valid
21.0ms	496×	body	80	nan
10.0ms	118×	body	160	valid
7.0ms	155×	body	80	invalid

Details

sample1.2s

simplify350.0ms

prune5.0ms

localize24.0ms

rewrite29.0ms

series69.0ms

simplify139.0ms

prune140.0ms

localize12.0ms

rewrite53.0ms

series121.0ms

simplify110.0ms

prune224.0ms

localize12.0ms

rewrite29.0ms

series76.0ms

simplify50.0ms

prune93.0ms

localize12.0ms

rewrite28.0ms

series80.0ms

simplify38.0ms

prune86.0ms

regimes373.0ms

bsearch145.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling