Details

sample44.0ms

Algorithm

intervals

Results

11.0ms	38×	body	2560	valid
9.0ms	188×	body	80	valid
5.0ms	256×	pre	80	true
3.0ms	11×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 13.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
18.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
286.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	242	529
1	853	492
2	2977	488
3	5002	487

prune192.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	8	64

Merged error: 13.0b

Counts

64 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.8b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
7×	`sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `unpow2` `sqr-pow`
3×	`flip3-+` `div-exp` `associate-/r*` `flip-+` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 97

Calls

4 calls:

12.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	325	1030
1	1289	956
2	5001	954

prune401.0ms

Filtered

109 candidates to 81 candidates (74.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	109	8	117

Merged error: 13.0b

Counts

117 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite20.0ms

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` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify85.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune372.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	71	9	80

Merged error: 13.0b

Counts

80 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.1b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
70.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	290	1356
1	1084	1258
2	5001	1216

prune275.0ms

Filtered

137 candidates to 76 candidates (55.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	135	11	146

Merged error: 13.0b

Counts

146 → 11

regimes182.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.5b and baseline of 13.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	27
1	31	27

end0.0ms

sample1.1s

Algorithm

intervals

Results

287.0ms	5958×	body	80	valid
252.0ms	824×	body	2560	valid
160.0ms	628×	body	1280	valid
132.0ms	8000×	pre	80	true
66.0ms	353×	body	640	valid
21.0ms	152×	body	320	valid
8.0ms	85×	body	160	valid

Details

sample44.0ms

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite40.0ms

series453.0ms

simplify90.0ms

prune192.0ms

localize23.0ms

rewrite37.0ms

series245.0ms

simplify47.0ms

prune401.0ms

localize23.0ms

rewrite20.0ms

series227.0ms

simplify85.0ms

prune372.0ms

localize14.0ms

rewrite39.0ms

series245.0ms

simplify53.0ms

prune275.0ms

regimes182.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

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