Details

analyze505.0ms

Algorithm: search

sample37.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	19×	body	80	nan
1.0ms	11×	body	80	invalid

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

prune5.0ms

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: 18.4b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	248	644
1	898	606
2	3863	590
3	5001	586

prune185.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Merged error: 6.9b

Counts

76 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

13.2b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(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))))))
3.0ms	(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))))))
13.0ms	(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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (98.0ms)

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

prune198.0ms

Filtered

59 candidates to 72 candidates (-22.0%)

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: 6.9b

Counts

78 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

7.6b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(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:

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

series97.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (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)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (35.0ms)

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

prune226.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	66	6	72

Merged error: 6.9b

Counts

72 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

22.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

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

series97.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(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)))

simplify74.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	171	672
1	559	628
2	2234	604
3	5001	572

prune265.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	64	6	70

Merged error: 6.9b

Counts

70 → 6

regimes244.0ms

Accuracy

93.8% (0.8b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 20.0b

bsearch574.0ms

Steps

Iters	Range		Point
9	5.117647322556711e+132	9.392231666819859e+139	3.051485498805635e+137
9	-3.9643206768272174e+161	-5.7762132568993676e+153	-1.3677415519136428e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

analyze509.0ms

Algorithm: search

sample988.0ms

Algorithm

intervals

Results

703.0ms	8000×	body	80	valid
54.0ms	647×	body	80	nan
33.0ms	390×	body	80	invalid

Details

analyze505.0ms

sample37.0ms

simplify13.0ms

prune5.0ms

localize22.0ms

rewrite27.0ms

series70.0ms

simplify116.0ms

prune185.0ms

localize24.0ms

rewrite16.0ms

series58.0ms

simplify106.0ms

prune198.0ms

localize25.0ms

rewrite17.0ms

series97.0ms

simplify43.0ms

prune226.0ms

localize35.0ms

rewrite15.0ms

series97.0ms

simplify74.0ms

prune265.0ms

regimes244.0ms

bsearch574.0ms

simplify2.0ms

end0.0ms

analyze509.0ms

sample988.0ms

Profiling