Details

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.466919%

Guaranteed chance to sample good point: 84.821684%

Results

23.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid
1.0ms	11×	body	80	nan

simplify350.0ms

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: 19.7b

Counts

2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(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	3865	590
3	5001	586

prune205.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	8	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Merged error: 7.8b

Counts

76 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

12.5b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

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:

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)))

series63.0ms

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

simplify115.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	227	677
1	876	574
2	3665	562
3	5003	558

prune219.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 7.8b

Counts

78 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

5.7b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(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` `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))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
28.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (35.0ms)

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

prune243.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 7.8b

Counts

75 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
32.7b	(cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`sqrt-prod`
11×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1` `unpow-prod-down` `sqrt-div` `cube-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`cube-div` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `cube-mult` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `pow1/3` `unpow3` `neg-log` `rem-cbrt-cube` `flip-+` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+ (neg b) (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)))
6.0ms	(cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))

series62.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (neg b) (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)))
15.0ms	(cbrt (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))

simplify39.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	308	688
1	1259	664
2	5001	652

prune169.0ms

Filtered

62 candidates to 86 candidates (-38.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	86	9	95

Merged error: 7.8b

Counts

95 → 9

regimes334.0ms

Accuracy

91.9% (0.9b remaining)

Error of 8.9b against oracle of 7.9b and baseline of 19.5b

bsearch124.0ms

Steps

Iters	Range		Point
9	1.5459895330698598e+151	3.530700376421774e+156	2.0252423076498904e+151
9	-2.2921502228163733e+164	-2.9988818969355234e+157	-3.060284484342092e+157

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	58
1	49	58

end0.0ms

sample4.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.466919%

Guaranteed chance to sample good point: 84.821684%

Results

698.0ms	8000×	body	80	valid
31.0ms	377×	body	80	nan
27.0ms	324×	body	80	invalid

Details

sample3.4s

simplify350.0ms

prune6.0ms

localize35.0ms

rewrite28.0ms

series75.0ms

simplify116.0ms

prune205.0ms

localize25.0ms

rewrite17.0ms

series63.0ms

simplify115.0ms

prune219.0ms

localize29.0ms

rewrite17.0ms

series108.0ms

simplify44.0ms

prune243.0ms

localize27.0ms

rewrite23.0ms

series62.0ms

simplify39.0ms

prune169.0ms

regimes334.0ms

bsearch124.0ms

simplify3.0ms

end0.0ms

sample4.3s

Profiling