Details

sample624.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 44.117754%

Results

24.0ms	277×	body	80	valid
5.0ms	67×	body	80	nan

simplify346.0ms

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: 20.9b

Counts

2 → 1

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (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)))

simplify117.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (109.0ms)

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

prune203.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	9	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	9	76

Merged error: 7.4b

Counts

76 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

10.6b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

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))))))
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)))

series60.0ms

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)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (105.0ms)

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

prune213.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	70	9	79

Merged error: 7.4b

Counts

79 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

series61.0ms

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

simplify100.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	204	609
1	755	588
2	3222	580
3	5002	576

prune219.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	75	9	84

Merged error: 7.4b

Counts

84 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

5.8b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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:

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (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)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(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

prune200.0ms

Filtered

60 candidates to 67 candidates (-11.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	67	9	76

Merged error: 7.4b

Counts

76 → 9

regimes293.0ms

Accuracy

92.6% (0.9b remaining)

Error of 8.7b against oracle of 7.8b and baseline of 20.0b

bsearch67.0ms

Steps

Iters	Range		Point
7	1.2782701051242085e+124	3.366651077321003e+125	1.4075340652414269e+125
9	-3.6360618111710883e+118	-7.710355295872846e+111	-3.2424478290772433e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	58
1	49	58

end0.0ms

sample1.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 44.117754%

Results

752.0ms	8757×	body	80	valid
177.0ms	2217×	body	80	nan

Details

sample624.0ms

simplify346.0ms

prune6.0ms

localize36.0ms

rewrite27.0ms

series73.0ms

simplify117.0ms

prune203.0ms

localize24.0ms

rewrite16.0ms

series60.0ms

simplify113.0ms

prune213.0ms

localize26.0ms

rewrite21.0ms

series61.0ms

simplify100.0ms

prune219.0ms

localize25.0ms

rewrite18.0ms

series103.0ms

simplify44.0ms

prune200.0ms

regimes293.0ms

bsearch67.0ms

simplify2.0ms

end0.0ms

sample1.7s

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