Details

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.306274%

Guaranteed chance to sample good point: 82.125662%

Results

22.0ms	256×	body	80	valid
2.0ms	25×	body	80	invalid
1.0ms	14×	body	80	nan

simplify17.0ms

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

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: 19.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.9b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

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:

8.0ms	(+ (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)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(- (neg b) (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)))

simplify114.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (106.0ms)

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

prune201.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	65	10	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	10	76

Merged error: 7.4b

Counts

76 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

9.3b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.3b	(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))))))
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)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (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)))

simplify41.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (33.0ms)

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

prune256.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	66	11	77

Merged error: 7.3b

Counts

77 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

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

series70.0ms

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)))
27.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	218	570
1	680	547
2	2689	538
3	5002	527

prune285.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	70	11	81

Merged error: 7.3b

Counts

81 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(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:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(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)))

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

prune232.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	72	11	83

Merged error: 7.3b

Counts

83 → 11

regimes344.0ms

Accuracy

92.6% (0.9b remaining)

Error of 8.6b against oracle of 7.6b and baseline of 20.1b

bsearch65.0ms

Steps

Iters	Range		Point
7	4.117318380954776e+122	2.407345990094287e+124	1.0296911536192026e+123
8	-1.11355135107887e+150	-2.8449590834025068e+147	-1.0998363878598405e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	59
1	54	59

end0.0ms

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.306274%

Guaranteed chance to sample good point: 82.125662%

Results

703.0ms	8000×	body	80	valid
53.0ms	637×	body	80	invalid
31.0ms	383×	body	80	nan

Details

sample1.5s

simplify17.0ms

prune4.0ms

localize21.0ms

rewrite25.0ms

series62.0ms

simplify114.0ms

prune201.0ms

localize28.0ms

rewrite16.0ms

series101.0ms

simplify41.0ms

prune256.0ms

localize29.0ms

rewrite16.0ms

series70.0ms

simplify81.0ms

prune285.0ms

localize26.0ms

rewrite16.0ms

series58.0ms

simplify67.0ms

prune232.0ms

regimes344.0ms

bsearch65.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling