Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	39×	body	2560	valid
9.0ms	175×	body	80	valid
5.0ms	20×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	16×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify8.0ms

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

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: 16.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series25.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify77.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	203	365
1	753	336
2	2672	332
3	5002	331

prune122.0ms

Filtered

38 candidates to 47 candidates (-23.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	9	48

Merged error: 16.0b

Counts

48 → 9

localize13.0ms

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)))))
9.7b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

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:

18.0ms	(* (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)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (34.0ms)

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

prune237.0ms

Filtered

72 candidates to 137 candidates (-90.3%)

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: 16.0b

Counts

146 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

12.6b	(sqrt (* (* (cbrt (+ (* (* 4.0 p) p) (* x x))) (cbrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (+ (* (* 4.0 p) p) (* x x)))))
13.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

19.0ms	(sqrt (* (* (cbrt (+ (* (* 4.0 p) p) (* x x))) (cbrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (* (* (cbrt (+ (* (* 4.0 p) p) (* x x))) (cbrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (+ (* (* 4.0 p) p) (* x x)))))
21.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
21.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
21.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify164.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	325	1861
1	757	1811
2	3545	1792
3	5003	1690

prune257.0ms

Filtered

66 candidates to 101 candidates (-53.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	99	13	112

Merged error: 16.0b

Counts

112 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

13.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.4b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite20.0ms

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:

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

series87.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
21.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
21.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	156	652
1	431	608
2	1509	600
3	5002	568

prune293.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	3	7	10
Picked	0	1	1
Done	0	2	2
Total	65	12	77

Merged error: 16.0b

Counts

77 → 12

regimes609.0ms

Accuracy

0% (0.2b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	9
1	19	9

end0.0ms

sample1.2s

Algorithm

intervals

Results

302.0ms	6008×	body	80	valid
252.0ms	814×	body	2560	valid
155.0ms	629×	body	1280	valid
135.0ms	8000×	pre	80	true
64.0ms	308×	body	640	valid
23.0ms	156×	body	320	valid
8.0ms	85×	body	160	valid

Details

sample46.0ms

simplify8.0ms

prune3.0ms

localize10.0ms

rewrite25.0ms

series25.0ms

simplify77.0ms

prune122.0ms

localize13.0ms

rewrite41.0ms

series34.0ms

simplify49.0ms

prune237.0ms

localize15.0ms

rewrite38.0ms

series72.0ms

simplify164.0ms

prune257.0ms

localize19.0ms

rewrite20.0ms

series87.0ms

simplify56.0ms

prune293.0ms

regimes609.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling