Details

sample18.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	70×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

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: 26.4b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

24.6b

(sqrt (+ (* x x) y))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

4.0ms

(sqrt (+ (* x x) y))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(sqrt (+ (* x x) y))

simplify35.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4955	159
1	4955	159

prune29.0ms

Filtered

15 candidates to 18 candidates (-20.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Merged error: 0b

Counts

19 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* x x) y)))
0.3b	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
25.5b	(cbrt (+ (* x x) y))
25.5b	(cbrt (+ (* x x) y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

7.0ms	(sqrt (cbrt (+ (* x x) y)))
9.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
4.0ms	(cbrt (+ (* x x) y))
4.0ms	(cbrt (+ (* x x) y))

series77.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (cbrt (+ (* x x) y)))
27.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
17.0ms	(cbrt (+ (* x x) y))
17.0ms	(cbrt (+ (* x x) y))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4944	1019
1	4944	1019

prune84.0ms

Filtered

65 candidates to 86 candidates (-32.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	86	4	90

Merged error: 0b

Counts

90 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (/ 1/2 x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

6.0ms

(* y (/ 1/2 x))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* y (/ 1/2 x))

simplify50.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5100	229

prune36.0ms

Filtered

24 candidates to 35 candidates (-45.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	35	4	39

Merged error: 0b

Counts

39 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (/ -1/2 x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

6.0ms

(* y (/ -1/2 x))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* y (/ -1/2 x))

simplify57.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5299	230

prune34.0ms

Filtered

24 candidates to 35 candidates (-45.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	35	4	39

Merged error: 0b

Counts

39 → 4

regimes274.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.6b

bsearch24.0ms

Steps

Iters	Range		Point
6	5.751584421923189e+65	4.459352800688635e+66	4.3814772908188566e+66
10	-1.6796181841493287e+154	-3.4073642768570884e+140	-1.3522080438574694e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	28
1	23	28

end0.0ms

sample510.0ms

Algorithm

intervals

Results

196.0ms	8000×	body	80	valid
61.0ms	2607×	body	80	nan

Details

sample18.0ms

simplify3.0ms

prune6.0ms

localize4.0ms

rewrite4.0ms

series6.0ms

simplify35.0ms

prune29.0ms

localize8.0ms

rewrite26.0ms

series77.0ms

simplify41.0ms

prune84.0ms

localize4.0ms

rewrite8.0ms

series3.0ms

simplify50.0ms

prune36.0ms

localize5.0ms

rewrite8.0ms

series3.0ms

simplify57.0ms

prune34.0ms

regimes274.0ms

bsearch24.0ms

simplify1.0ms

end0.0ms

sample510.0ms

Profiling