Details

analyze739.0ms

Algorithm: search

sample44.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
2.0ms	25×	body	80	nan
1.0ms	10×	body	80	invalid

simplify372.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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: 19.7b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (* b b) (* (* 4.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(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))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (* 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 (73.0ms)

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

prune170.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 8.6b

Counts

67 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

8.2b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`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` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 60

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)))

series60.0ms

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

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	221	722
1	829	631
2	3533	612
3	5001	592

prune217.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 8.6b

Counts

80 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

9.5b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.9b	(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` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 54

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

series100.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	382	836
1	1428	761
2	5002	721

prune233.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Merged error: 8.6b

Counts

72 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

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)))
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

prune238.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	71	7	78

Merged error: 8.6b

Counts

78 → 7

regimes272.0ms

Accuracy

91.1% (1.1b remaining)

Error of 8.9b against oracle of 7.8b and baseline of 19.8b

bsearch641.0ms

Steps

Iters	Range		Point
8	1.6918924581089582e+84	1.0279369873624978e+87	9.661652465048311e+86
10	-3.289975268518999e+90	-1.4541948919297818e+74	-3.019784171445724e+90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	59
1	55	59

end0.0ms

analyze518.0ms

Algorithm: search

sample1.0s

Algorithm

intervals

Results

722.0ms	8000×	body	80	valid
55.0ms	666×	body	80	nan
33.0ms	384×	body	80	invalid

Details

analyze739.0ms

sample44.0ms

simplify372.0ms

prune6.0ms

localize25.0ms

rewrite19.0ms

series59.0ms

simplify80.0ms

prune170.0ms

localize24.0ms

rewrite17.0ms

series60.0ms

simplify108.0ms

prune217.0ms

localize29.0ms

rewrite16.0ms

series100.0ms

simplify43.0ms

prune233.0ms

localize28.0ms

rewrite16.0ms

series58.0ms

simplify67.0ms

prune238.0ms

regimes272.0ms

bsearch641.0ms

simplify2.0ms

end0.0ms

analyze518.0ms

sample1.0s

Profiling