Details

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 25.539477%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

12.0ms	47×	body	2560	valid
7.0ms	156×	body	80	valid
6.0ms	27×	body	1280	valid
3.0ms	11×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	15×	body	80	nan
0.0ms	4×	body	160	valid
0.0ms	3×	body	80	invalid

simplify369.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 36.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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:

9.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (+ (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)))

simplify140.0ms

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

prune133.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 5.6b

Counts

93 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.6b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

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:

10.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
48.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (80.0ms)

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

prune228.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	217	8	225

Merged error: 5.5b

Counts

225 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.8b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
25.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
49.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
47.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune311.0ms

Filtered

303 candidates to 503 candidates (-66.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	501	2	503
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	503	8	511

Merged error: 5.5b

Counts

511 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
0.6b	(- (* b_2 b_2) (* a c))
0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
528×	`add-sqr-sqrt`
527×	`*-un-lft-identity`
355×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-rgt-neg-in` `div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 468

Calls

4 calls:

24.0ms	(/ (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
12.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

480 → 480

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1777	8958
1	5001	8170

prune280.0ms

Filtered

173 candidates to 480 candidates (-177.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	480	0	480
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	480	8	488

Merged error: 5.5b

Counts

488 → 8

regimes298.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.6b

bsearch134.0ms

Steps

Iters	Range	Point
9	4.129117031182218e+101	1.1861749358280942e+108	1.4390013145474845e+107
8	-6.205532804582912e-280	-2.0768182679900796e-283	-9.587510853226601e-281
9	-1.52074710287338e+108	-9.793190813429664e+100	-2.2217078168726145e+105

Iters

Range

Point

4.129117031182218e+101

1.1861749358280942e+108

1.4390013145474845e+107

-6.205532804582912e-280

-2.0768182679900796e-283

-9.587510853226601e-281

-1.52074710287338e+108

-9.793190813429664e+100

-2.2217078168726145e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 25.539477%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

277.0ms	1075×	body	2560	valid
222.0ms	5086×	body	80	valid
200.0ms	954×	body	1280	valid
71.0ms	442×	body	640	valid
35.0ms	113×	body	5120	valid
29.0ms	224×	body	320	valid
20.0ms	500×	body	80	nan
9.0ms	106×	body	160	valid
7.0ms	153×	body	80	invalid

Details

sample1.2s

simplify369.0ms

prune5.0ms

localize22.0ms

rewrite30.0ms

series62.0ms

simplify140.0ms

prune133.0ms

localize11.0ms

rewrite51.0ms

series117.0ms

simplify112.0ms

prune228.0ms

localize12.0ms

rewrite88.0ms

series123.0ms

simplify99.0ms

prune311.0ms

localize11.0ms

rewrite73.0ms

series66.0ms

simplify110.0ms

prune280.0ms

regimes298.0ms

bsearch134.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling