Details

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 22.631836%

Guaranteed chance to sample good point: 70.459924%

Results

11.0ms	154×	body	80	valid
9.0ms	35×	body	2560	valid
8.0ms	36×	body	1280	valid
3.0ms	19×	body	640	valid
1.0ms	22×	body	80	nan
1.0ms	16×	body	80	invalid
1.0ms	2×	body	5120	valid
1.0ms	6×	body	160	valid
0.0ms	4×	body	320	valid

simplify361.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

prune7.0ms

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: 39.5b

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)
0.2b	(- (* b_2 b_2) (* a c))
1.5b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

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:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- (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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune138.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 6.7b

Counts

104 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`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 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* 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)
40.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
58.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	704	2957
1	3098	2807
2	5001	2787

prune240.0ms

Filtered

148 candidates to 199 candidates (-34.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	193	6	199
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	197	10	207

Merged error: 6.5b

Counts

207 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.1b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
549×	`add-sqr-sqrt`
450×	`*-un-lft-identity`
352×	`add-cube-cbrt`
98×	`difference-of-squares`
74×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 440

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
23.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
53.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
44.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1557	7387
1	5001	6822

prune314.0ms

Filtered

301 candidates to 452 candidates (-50.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	450	2	452
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	453	9	462

Merged error: 6.5b

Counts

462 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
0.3b	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

807×	`times-frac`
520×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
331×	`add-cube-cbrt`
94×	`difference-of-squares`
50×	`sqrt-prod`
48×	`add-exp-log`
47×	`distribute-lft-out--`
41×	`div-inv`
34×	`div-exp`
31×	`associate-/r/`
27×	`associate-/l*`
19×	`associate-/r*`
18×	`add-cbrt-cube`
17×	`flip3--` `flip--`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/` `inv-pow`

Counts

4 → 456

Calls

4 calls:

21.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
9.0ms	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
18.0ms	(/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

468 → 468

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1775	8061
1	5001	7321

prune313.0ms

Filtered

188 candidates to 468 candidates (-148.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	467	1	468
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	468	9	477

Merged error: 6.5b

Counts

477 → 9

regimes319.0ms

Accuracy

79.2% (5.0b remaining)

Error of 10.7b against oracle of 5.7b and baseline of 29.9b

bsearch67.0ms

Steps

Iters	Range		Point
9	2.904374354949655e-138	4.568446479967262e-131	2.7998310366975115e-131
7	-6.354608940524709e+74	-5.0242283959340966e+72	-5.244181346966041e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 22.631836%

Guaranteed chance to sample good point: 70.459924%

Results

259.0ms	1033×	body	2560	valid
230.0ms	5142×	body	80	valid
192.0ms	904×	body	1280	valid
78.0ms	466×	body	640	valid
34.0ms	111×	body	5120	valid
28.0ms	217×	body	320	valid
23.0ms	517×	body	80	invalid
21.0ms	503×	body	80	nan
10.0ms	127×	body	160	valid

Details

sample1.5s

simplify361.0ms

prune7.0ms

localize12.0ms

rewrite32.0ms

series66.0ms

simplify43.0ms

prune138.0ms

localize10.0ms

rewrite47.0ms

series125.0ms

simplify104.0ms

prune240.0ms

localize11.0ms

rewrite80.0ms

series123.0ms

simplify98.0ms

prune314.0ms

localize11.0ms

rewrite75.0ms

series71.0ms

simplify105.0ms

prune313.0ms

regimes319.0ms

bsearch67.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling