Details

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.466919%

Guaranteed chance to sample good point: 84.821684%

Results

25.0ms	256×	body	80	valid
1.0ms	15×	body	80	nan
1.0ms	13×	body	80	invalid

simplify365.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	18
1	66	18
2	116	18
3	144	18
4	159	18
5	161	18
6	161	18

prune6.0ms

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: 20.2b

Counts

2 → 1

localize44.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	147	476
1	564	446
2	2529	444
3	5002	442

prune166.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	7	67

Merged error: 10.6b

Counts

67 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

12.9b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

4.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	227	677
1	876	574
2	3665	562
3	5003	558

prune220.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 10.6b

Counts

77 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	127	536
1	460	520
2	1957	516
3	5001	512

prune308.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Merged error: 10.6b

Counts

79 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

6.5b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 55

Calls

4 calls:

4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	377	865
1	1397	791
2	5001	755

prune211.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	66	8	74

Merged error: 10.5b

Counts

74 → 8

regimes302.0ms

Accuracy

91.8% (1.0b remaining)

Error of 8.6b against oracle of 7.6b and baseline of 19.7b

bsearch108.0ms

Steps

Iters	Range		Point
8	1.0105943841455688e+106	1.3537691671318847e+109	3.860487157846461e+108
10	-3.953437756477324e+79	-1.9382075007119548e+62	-3.8702858868063573e+79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	74
1	57	74

end0.0ms

sample2.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.466919%

Guaranteed chance to sample good point: 84.821684%

Results

718.0ms	8000×	body	80	valid
29.0ms	356×	body	80	nan
25.0ms	294×	body	80	invalid

Details

sample1.5s

simplify365.0ms

prune6.0ms

localize44.0ms

rewrite19.0ms

series55.0ms

simplify82.0ms

prune166.0ms

localize24.0ms

rewrite17.0ms

series58.0ms

simplify115.0ms

prune220.0ms

localize33.0ms

rewrite17.0ms

series56.0ms

simplify67.0ms

prune308.0ms

localize29.0ms

rewrite16.0ms

series103.0ms

simplify42.0ms

prune211.0ms

regimes302.0ms

bsearch108.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling