Details

sample56.0ms

Algorithm

intervals

Results

25.0ms	281×	body	80	valid
7.0ms	84×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 17.8b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 60

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(- (neg b) (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)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	223	579
1	875	551
2	3958	543
3	5001	540

prune171.0ms

Filtered

72 candidates to 55 candidates (23.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 6.7b

Counts

73 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

12.6b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

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)))

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

simplify105.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (97.0ms)

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

prune203.0ms

Filtered

72 candidates to 59 candidates (18.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 6.7b

Counts

78 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

5.0b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

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:

6.0ms	(+ (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)))

series95.0ms

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))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	382	835
1	1434	761
2	5002	721

prune231.0ms

Filtered

66 candidates to 60 candidates (9.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	65	7	72

Merged error: 6.7b

Counts

72 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

5.0ms	(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)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	218	638
1	680	601
2	2689	582
3	5002	557

prune208.0ms

Filtered

66 candidates to 57 candidates (13.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	66	7	73

Merged error: 6.7b

Counts

73 → 7

regimes265.0ms

Accuracy

93.2% (0.8b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 19.8b

bsearch66.0ms

Steps

Iters	Range		Point
9	3.740966656805541e+90	2.271321644956683e+99	1.0706833997838064e+97
8	-1.795609024723082e+157	-2.0984588557191883e+153	-1.3277288429394208e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	59
1	51	59

end0.0ms

sample1.4s

Algorithm

intervals

Results

769.0ms	8730×	body	80	valid
231.0ms	2788×	body	80	nan

Details

sample56.0ms

simplify13.0ms

prune4.0ms

localize23.0ms

rewrite23.0ms

series53.0ms

simplify120.0ms

prune171.0ms

localize24.0ms

rewrite16.0ms

series58.0ms

simplify105.0ms

prune203.0ms

localize26.0ms

rewrite17.0ms

series95.0ms

simplify41.0ms

prune231.0ms

localize26.0ms

rewrite16.0ms

series86.0ms

simplify77.0ms

prune208.0ms

regimes265.0ms

bsearch66.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling