Details

analyze731.0ms

Algorithm: search

sample41.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
3.0ms	33×	body	80	nan
1.0ms	12×	body	80	invalid

simplify358.0ms

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: 16.9b

Counts

2 → 1

localize43.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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

series54.0ms

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)))

simplify80.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	147	474
1	570	446
2	2550	444
3	5001	442

prune188.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	54	12	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	12	67

Merged error: 7.1b

Counts

67 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

11.1b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify111.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (104.0ms)

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

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Merged error: 7.1b

Counts

82 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(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)))

series59.0ms

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)))
16.0ms	(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

prune309.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Merged error: 7.1b

Counts

80 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

6.7b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.6b	(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))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (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)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
28.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	377	866
1	1391	791
2	5001	755

prune207.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	66	9	75

Merged error: 7.1b

Counts

75 → 9

regimes276.0ms

Accuracy

86.8% (1.6b remaining)

Error of 9.2b against oracle of 7.6b and baseline of 19.7b

bsearch515.0ms

Steps

Iters	Range		Point
8	3.5726146118531287e+18	2.2397022699456155e+21	2.2181478789785576e+21
7	-4.8908751238470227e+154	-1.1156176474700752e+153	-2.8206609508134856e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	73
1	58	73

end0.0ms

analyze500.0ms

Algorithm: search

sample982.0ms

Algorithm

intervals

Results

698.0ms	8000×	body	80	valid
59.0ms	700×	body	80	nan
31.0ms	379×	body	80	invalid

Details

analyze731.0ms

sample41.0ms

simplify358.0ms

prune6.0ms

localize43.0ms

rewrite18.0ms

series54.0ms

simplify80.0ms

prune188.0ms

localize23.0ms

rewrite18.0ms

series59.0ms

simplify111.0ms

prune220.0ms

localize31.0ms

rewrite17.0ms

series59.0ms

simplify67.0ms

prune309.0ms

localize26.0ms

rewrite16.0ms

series101.0ms

simplify41.0ms

prune207.0ms

regimes276.0ms

bsearch515.0ms

simplify2.0ms

end0.0ms

analyze500.0ms

sample982.0ms

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